/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 175 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 49.8 s] (14) BOUNDS(1, INF) (15) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (16) CpxTRS (17) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (18) CpxRelTRS (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) NarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (26) CpxTypedWeightedCompleteTrs (27) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) SimplificationProof [BOTH BOUNDS(ID, ID), 4 ms] (30) CpxRNTS (31) CompletionProof [UPPER BOUND(ID), 0 ms] (32) CpxTypedWeightedCompleteTrs (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (36) CdtProblem (37) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (44) CdtProblem (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (46) CdtProblem (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (54) CdtProblem (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (56) CdtProblem (57) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 8 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 57 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (98) CdtProblem (99) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (106) CdtProblem (107) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (110) CdtProblem (111) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 10 ms] (112) CdtProblem (113) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms] (118) CdtProblem (119) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 17 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (128) CdtProblem (129) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 7 ms] (132) CdtProblem (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 151 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 4 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms] (144) CdtProblem (145) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (164) CdtProblem (165) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 104 ms] (172) CdtProblem (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (176) CdtProblem (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (184) CdtProblem (185) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (186) CdtProblem ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) The (relative) TRS S consists of the following rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome Rewrite Strategy: INNERMOST ---------------------------------------- (3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) The (relative) TRS S consists of the following rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome Rewrite Strategy: INNERMOST ---------------------------------------- (5) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (6) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) The (relative) TRS S consists of the following rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome Rewrite Strategy: INNERMOST ---------------------------------------- (7) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) The (relative) TRS S consists of the following rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome Rewrite Strategy: INNERMOST ---------------------------------------- (9) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (10) Obligation: Innermost TRS: Rules: app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome Types: app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app and :: and:true:false:or:forall:nil:cons:forsome:cons_app true :: and:true:false:or:forall:nil:cons:forsome:cons_app false :: and:true:false:or:forall:nil:cons:forsome:cons_app or :: and:true:false:or:forall:nil:cons:forsome:cons_app forall :: and:true:false:or:forall:nil:cons:forsome:cons_app nil :: and:true:false:or:forall:nil:cons:forsome:cons_app cons :: and:true:false:or:forall:nil:cons:forsome:cons_app forsome :: and:true:false:or:forall:nil:cons:forsome:cons_app encArg :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app cons_app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app encode_app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app encode_and :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_true :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_false :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_or :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_forall :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_nil :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_cons :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_forsome :: and:true:false:or:forall:nil:cons:forsome:cons_app hole_and:true:false:or:forall:nil:cons:forsome:cons_app1_0 :: and:true:false:or:forall:nil:cons:forsome:cons_app gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0 :: Nat -> and:true:false:or:forall:nil:cons:forsome:cons_app ---------------------------------------- (11) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: app, encArg They will be analysed ascendingly in the following order: app < encArg ---------------------------------------- (12) Obligation: Innermost TRS: Rules: app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome Types: app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app and :: and:true:false:or:forall:nil:cons:forsome:cons_app true :: and:true:false:or:forall:nil:cons:forsome:cons_app false :: and:true:false:or:forall:nil:cons:forsome:cons_app or :: and:true:false:or:forall:nil:cons:forsome:cons_app forall :: and:true:false:or:forall:nil:cons:forsome:cons_app nil :: and:true:false:or:forall:nil:cons:forsome:cons_app cons :: and:true:false:or:forall:nil:cons:forsome:cons_app forsome :: and:true:false:or:forall:nil:cons:forsome:cons_app encArg :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app cons_app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app encode_app :: and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app -> and:true:false:or:forall:nil:cons:forsome:cons_app encode_and :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_true :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_false :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_or :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_forall :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_nil :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_cons :: and:true:false:or:forall:nil:cons:forsome:cons_app encode_forsome :: and:true:false:or:forall:nil:cons:forsome:cons_app hole_and:true:false:or:forall:nil:cons:forsome:cons_app1_0 :: and:true:false:or:forall:nil:cons:forsome:cons_app gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0 :: Nat -> and:true:false:or:forall:nil:cons:forsome:cons_app Generator Equations: gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(0) <=> and gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(+(x, 1)) <=> cons_app(and, gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(x)) The following defined symbols remain to be analysed: app, encArg They will be analysed ascendingly in the following order: app < encArg ---------------------------------------- (13) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(n46874_0)) -> *3_0, rt in Omega(0) Induction Base: encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(0)) Induction Step: encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(+(n46874_0, 1))) ->_R^Omega(0) app(encArg(and), encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(n46874_0))) ->_R^Omega(0) app(and, encArg(gen_and:true:false:or:forall:nil:cons:forsome:cons_app2_0(n46874_0))) ->_IH app(and, *3_0) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (14) BOUNDS(1, INF) ---------------------------------------- (15) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (16) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, p), nil) -> true app(app(forall, p), app(app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(app(forsome, p), nil) -> false app(app(forsome, p), app(app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (17) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (18) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(c_app(and, false), true) -> false app(c_app(forsome, p), nil) -> false app(c_app(and, true), true) -> true app(c_app(or, false), true) -> true app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) app(c_app(or, true), true) -> true app(c_app(and, true), false) -> false app(c_app(forall, p), nil) -> true app(c_app(or, true), false) -> true app(c_app(and, false), false) -> false app(c_app(or, false), false) -> false app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) The (relative) TRS S consists of the following rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome app(x0, x1) -> c_app(x0, x1) Rewrite Strategy: INNERMOST ---------------------------------------- (19) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (20) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: app(c_app(and, false), true) -> false [1] app(c_app(forsome, p), nil) -> false [1] app(c_app(and, true), true) -> true [1] app(c_app(or, false), true) -> true [1] app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1] app(c_app(or, true), true) -> true [1] app(c_app(and, true), false) -> false [1] app(c_app(forall, p), nil) -> true [1] app(c_app(or, true), false) -> true [1] app(c_app(and, false), false) -> false [1] app(c_app(or, false), false) -> false [1] app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1] encArg(and) -> and [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(or) -> or [0] encArg(forall) -> forall [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(forsome) -> forsome [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_and -> and [0] encode_true -> true [0] encode_false -> false [0] encode_or -> or [0] encode_forall -> forall [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_forsome -> forsome [0] app(x0, x1) -> c_app(x0, x1) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(c_app(and, false), true) -> false [1] app(c_app(forsome, p), nil) -> false [1] app(c_app(and, true), true) -> true [1] app(c_app(or, false), true) -> true [1] app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1] app(c_app(or, true), true) -> true [1] app(c_app(and, true), false) -> false [1] app(c_app(forall, p), nil) -> true [1] app(c_app(or, true), false) -> true [1] app(c_app(and, false), false) -> false [1] app(c_app(or, false), false) -> false [1] app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1] encArg(and) -> and [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(or) -> or [0] encArg(forall) -> forall [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(forsome) -> forsome [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_and -> and [0] encode_true -> true [0] encode_false -> false [0] encode_or -> or [0] encode_forall -> forall [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_forsome -> forsome [0] app(x0, x1) -> c_app(x0, x1) [0] The TRS has the following type information: app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app c_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encArg :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app cons_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app encode_forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app Rewrite Strategy: INNERMOST ---------------------------------------- (23) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: encArg_1 encode_app_2 encode_and encode_true encode_false encode_or encode_forall encode_nil encode_cons encode_forsome app_2 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_and -> null_encode_and [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_or -> null_encode_or [0] encode_forall -> null_encode_forall [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_forsome -> null_encode_forsome [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_and, null_encode_true, null_encode_false, null_encode_or, null_encode_forall, null_encode_nil, null_encode_cons, null_encode_forsome, null_app ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(c_app(and, false), true) -> false [1] app(c_app(forsome, p), nil) -> false [1] app(c_app(and, true), true) -> true [1] app(c_app(or, false), true) -> true [1] app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1] app(c_app(or, true), true) -> true [1] app(c_app(and, true), false) -> false [1] app(c_app(forall, p), nil) -> true [1] app(c_app(or, true), false) -> true [1] app(c_app(and, false), false) -> false [1] app(c_app(or, false), false) -> false [1] app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1] encArg(and) -> and [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(or) -> or [0] encArg(forall) -> forall [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(forsome) -> forsome [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_and -> and [0] encode_true -> true [0] encode_false -> false [0] encode_or -> or [0] encode_forall -> forall [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_forsome -> forsome [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_and -> null_encode_and [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_or -> null_encode_or [0] encode_forall -> null_encode_forall [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_forsome -> null_encode_forsome [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app c_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encArg :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app cons_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encArg :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (25) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (26) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(c_app(and, false), true) -> false [1] app(c_app(forsome, p), nil) -> false [1] app(c_app(and, true), true) -> true [1] app(c_app(or, false), true) -> true [1] app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1] app(c_app(or, true), true) -> true [1] app(c_app(and, true), false) -> false [1] app(c_app(forall, p), nil) -> true [1] app(c_app(or, true), false) -> true [1] app(c_app(and, false), false) -> false [1] app(c_app(or, false), false) -> false [1] app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1] encArg(and) -> and [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(or) -> or [0] encArg(forall) -> forall [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(forsome) -> forsome [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_and -> and [0] encode_true -> true [0] encode_false -> false [0] encode_or -> or [0] encode_forall -> forall [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_forsome -> forsome [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_and -> null_encode_and [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_or -> null_encode_or [0] encode_forall -> null_encode_forall [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_forsome -> null_encode_forsome [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app c_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encArg :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app cons_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encArg :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (27) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: and => 0 false => 2 true => 7 forsome => 4 nil => 5 or => 6 forall => 3 cons => 1 null_encArg => 0 null_encode_app => 0 null_encode_and => 0 null_encode_true => 0 null_encode_false => 0 null_encode_or => 0 null_encode_forall => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_forsome => 0 null_app => 0 ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 1 }-> app(app(6, app(p, x)), app(app(4, p), xs)) :|: xs >= 0, x >= 0, p >= 0, z = 1 + 4 + p, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(app(0, app(p, x)), app(app(3, p), xs)) :|: xs >= 0, x >= 0, z = 1 + 3 + p, p >= 0, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> 7 :|: z = 1 + 0 + 7, z' = 7 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 2, z' = 7 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, z' = 7 app(z, z') -{ 1 }-> 7 :|: z = 1 + 3 + p, p >= 0, z' = 5 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, z' = 2 app(z, z') -{ 1 }-> 2 :|: z = 1 + 0 + 2, z' = 7 app(z, z') -{ 1 }-> 2 :|: p >= 0, z = 1 + 4 + p, z' = 5 app(z, z') -{ 1 }-> 2 :|: z' = 2, z = 1 + 0 + 7 app(z, z') -{ 1 }-> 2 :|: z' = 2, z = 1 + 0 + 2 app(z, z') -{ 1 }-> 2 :|: z = 1 + 6 + 2, z' = 2 app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 7 :|: z = 7 encArg(z) -{ 0 }-> 6 :|: z = 6 encArg(z) -{ 0 }-> 5 :|: z = 5 encArg(z) -{ 0 }-> 4 :|: z = 4 encArg(z) -{ 0 }-> 3 :|: z = 3 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_and -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 2 :|: encode_false -{ 0 }-> 0 :|: encode_forall -{ 0 }-> 3 :|: encode_forall -{ 0 }-> 0 :|: encode_forsome -{ 0 }-> 4 :|: encode_forsome -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 5 :|: encode_nil -{ 0 }-> 0 :|: encode_or -{ 0 }-> 6 :|: encode_or -{ 0 }-> 0 :|: encode_true -{ 0 }-> 7 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (29) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (30) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 1 }-> app(app(6, app(z - 5, x)), app(app(4, z - 5), xs)) :|: xs >= 0, x >= 0, z - 5 >= 0, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(app(0, app(z - 4, x)), app(app(3, z - 4), xs)) :|: xs >= 0, x >= 0, z - 4 >= 0, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> 7 :|: z = 1 + 0 + 7, z' = 7 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 2, z' = 7 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, z' = 7 app(z, z') -{ 1 }-> 7 :|: z - 4 >= 0, z' = 5 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, z' = 2 app(z, z') -{ 1 }-> 2 :|: z = 1 + 0 + 2, z' = 7 app(z, z') -{ 1 }-> 2 :|: z - 5 >= 0, z' = 5 app(z, z') -{ 1 }-> 2 :|: z' = 2, z = 1 + 0 + 7 app(z, z') -{ 1 }-> 2 :|: z' = 2, z = 1 + 0 + 2 app(z, z') -{ 1 }-> 2 :|: z = 1 + 6 + 2, z' = 2 app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 app(z, z') -{ 0 }-> 1 + z + z' :|: z >= 0, z' >= 0 encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 7 :|: z = 7 encArg(z) -{ 0 }-> 6 :|: z = 6 encArg(z) -{ 0 }-> 5 :|: z = 5 encArg(z) -{ 0 }-> 4 :|: z = 4 encArg(z) -{ 0 }-> 3 :|: z = 3 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: z >= 0 encode_and -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(z), encArg(z')) :|: z >= 0, z' >= 0 encode_app(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 2 :|: encode_false -{ 0 }-> 0 :|: encode_forall -{ 0 }-> 3 :|: encode_forall -{ 0 }-> 0 :|: encode_forsome -{ 0 }-> 4 :|: encode_forsome -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 5 :|: encode_nil -{ 0 }-> 0 :|: encode_or -{ 0 }-> 6 :|: encode_or -{ 0 }-> 0 :|: encode_true -{ 0 }-> 7 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (31) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_and -> null_encode_and [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_or -> null_encode_or [0] encode_forall -> null_encode_forall [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_forsome -> null_encode_forsome [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_and, null_encode_true, null_encode_false, null_encode_or, null_encode_forall, null_encode_nil, null_encode_cons, null_encode_forsome, null_app ---------------------------------------- (32) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(c_app(and, false), true) -> false [1] app(c_app(forsome, p), nil) -> false [1] app(c_app(and, true), true) -> true [1] app(c_app(or, false), true) -> true [1] app(c_app(forall, p), c_app(c_app(cons, x), xs)) -> app(app(and, app(p, x)), app(app(forall, p), xs)) [1] app(c_app(or, true), true) -> true [1] app(c_app(and, true), false) -> false [1] app(c_app(forall, p), nil) -> true [1] app(c_app(or, true), false) -> true [1] app(c_app(and, false), false) -> false [1] app(c_app(or, false), false) -> false [1] app(c_app(forsome, p), c_app(c_app(cons, x), xs)) -> app(app(or, app(p, x)), app(app(forsome, p), xs)) [1] encArg(and) -> and [0] encArg(true) -> true [0] encArg(false) -> false [0] encArg(or) -> or [0] encArg(forall) -> forall [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(forsome) -> forsome [0] encArg(cons_app(x_1, x_2)) -> app(encArg(x_1), encArg(x_2)) [0] encode_app(x_1, x_2) -> app(encArg(x_1), encArg(x_2)) [0] encode_and -> and [0] encode_true -> true [0] encode_false -> false [0] encode_or -> or [0] encode_forall -> forall [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_forsome -> forsome [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_and -> null_encode_and [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] encode_or -> null_encode_or [0] encode_forall -> null_encode_forall [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_forsome -> null_encode_forsome [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app c_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encArg :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app cons_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app -> and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app encode_forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encArg :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_and :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_true :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_false :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_or :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_forall :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_nil :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_cons :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_encode_forsome :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app null_app :: and:false:c_app:true:forsome:nil:or:forall:cons:cons_app:null_encArg:null_encode_app:null_encode_and:null_encode_true:null_encode_false:null_encode_or:null_encode_forall:null_encode_nil:null_encode_cons:null_encode_forsome:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (33) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: and => 0 false => 2 true => 7 forsome => 4 nil => 5 or => 6 forall => 3 cons => 1 null_encArg => 0 null_encode_app => 0 null_encode_and => 0 null_encode_true => 0 null_encode_false => 0 null_encode_or => 0 null_encode_forall => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_forsome => 0 null_app => 0 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 1 }-> app(app(6, app(p, x)), app(app(4, p), xs)) :|: xs >= 0, x >= 0, p >= 0, z = 1 + 4 + p, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> app(app(0, app(p, x)), app(app(3, p), xs)) :|: xs >= 0, x >= 0, z = 1 + 3 + p, p >= 0, z' = 1 + (1 + 1 + x) + xs app(z, z') -{ 1 }-> 7 :|: z = 1 + 0 + 7, z' = 7 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 2, z' = 7 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, z' = 7 app(z, z') -{ 1 }-> 7 :|: z = 1 + 3 + p, p >= 0, z' = 5 app(z, z') -{ 1 }-> 7 :|: z = 1 + 6 + 7, z' = 2 app(z, z') -{ 1 }-> 2 :|: z = 1 + 0 + 2, z' = 7 app(z, z') -{ 1 }-> 2 :|: p >= 0, z = 1 + 4 + p, z' = 5 app(z, z') -{ 1 }-> 2 :|: z' = 2, z = 1 + 0 + 7 app(z, z') -{ 1 }-> 2 :|: z' = 2, z = 1 + 0 + 2 app(z, z') -{ 1 }-> 2 :|: z = 1 + 6 + 2, z' = 2 app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 app(z, z') -{ 0 }-> 1 + x0 + x1 :|: z = x0, x0 >= 0, x1 >= 0, z' = x1 encArg(z) -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z = 1 + x_1 + x_2, x_2 >= 0 encArg(z) -{ 0 }-> 7 :|: z = 7 encArg(z) -{ 0 }-> 6 :|: z = 6 encArg(z) -{ 0 }-> 5 :|: z = 5 encArg(z) -{ 0 }-> 4 :|: z = 4 encArg(z) -{ 0 }-> 3 :|: z = 3 encArg(z) -{ 0 }-> 2 :|: z = 2 encArg(z) -{ 0 }-> 1 :|: z = 1 encArg(z) -{ 0 }-> 0 :|: z = 0 encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 encode_and -{ 0 }-> 0 :|: encode_app(z, z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z = x_1, z' = x_2 encode_app(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 encode_cons -{ 0 }-> 1 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 2 :|: encode_false -{ 0 }-> 0 :|: encode_forall -{ 0 }-> 3 :|: encode_forall -{ 0 }-> 0 :|: encode_forsome -{ 0 }-> 4 :|: encode_forsome -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 5 :|: encode_nil -{ 0 }-> 0 :|: encode_or -{ 0 }-> 6 :|: encode_or -{ 0 }-> 0 :|: encode_true -{ 0 }-> 7 :|: encode_true -{ 0 }-> 0 :|: Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (35) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: ENCARG(and) -> c ENCARG(true) -> c1 ENCARG(false) -> c2 ENCARG(or) -> c3 ENCARG(forall) -> c4 ENCARG(nil) -> c5 ENCARG(cons) -> c6 ENCARG(forsome) -> c7 ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_AND -> c10 ENCODE_TRUE -> c11 ENCODE_FALSE -> c12 ENCODE_OR -> c13 ENCODE_FORALL -> c14 ENCODE_NIL -> c15 ENCODE_CONS -> c16 ENCODE_FORSOME -> c17 APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(and, app(z0, z1)), APP(z0, z1), APP(app(forall, z0), z2), APP(forall, z0)) APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(or, app(z0, z1)), APP(z0, z1), APP(app(forsome, z0), z2), APP(forsome, z0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(and, app(z0, z1)), APP(z0, z1), APP(app(forall, z0), z2), APP(forall, z0)) APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(or, app(z0, z1)), APP(z0, z1), APP(app(forsome, z0), z2), APP(forsome, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, ENCODE_AND, ENCODE_TRUE, ENCODE_FALSE, ENCODE_OR, ENCODE_FORALL, ENCODE_NIL, ENCODE_CONS, ENCODE_FORSOME, APP_2 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8_3, c9_3, c10, c11, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27_5, c28, c29_5 ---------------------------------------- (37) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 16 trailing nodes: ENCODE_FORSOME -> c17 ENCODE_CONS -> c16 ENCARG(nil) -> c5 ENCODE_FALSE -> c12 ENCODE_FORALL -> c14 ENCODE_NIL -> c15 ENCARG(and) -> c ENCODE_OR -> c13 ENCODE_AND -> c10 ENCARG(true) -> c1 ENCARG(cons) -> c6 ENCARG(false) -> c2 ENCARG(forall) -> c4 ENCODE_TRUE -> c11 ENCARG(forsome) -> c7 ENCARG(or) -> c3 ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(and, app(z0, z1)), APP(z0, z1), APP(app(forall, z0), z2), APP(forall, z0)) APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(or, app(z0, z1)), APP(z0, z1), APP(app(forsome, z0), z2), APP(forsome, z0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(and, app(z0, z1)), APP(z0, z1), APP(app(forall, z0), z2), APP(forall, z0)) APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(or, app(z0, z1)), APP(z0, z1), APP(app(forsome, z0), z2), APP(forsome, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c8_3, c9_3, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27_5, c28, c29_5 ---------------------------------------- (39) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c9(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c8_3, c9_3, c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c27_3, c29_3 ---------------------------------------- (41) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCODE_APP(z0, z1) -> c(ENCARG(z0)) ENCODE_APP(z0, z1) -> c(ENCARG(z1)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c8_3, c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c27_3, c29_3, c_1 ---------------------------------------- (43) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_APP(z0, z1) -> c(ENCARG(z0)) ENCODE_APP(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_and, encode_true, encode_false, encode_or, encode_forall, encode_nil, encode_cons, encode_forsome Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c8_3, c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c27_3, c29_3, c_1 ---------------------------------------- (45) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_and -> and encode_true -> true encode_false -> false encode_or -> or encode_forall -> forall encode_nil -> nil encode_cons -> cons encode_forsome -> forsome ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c8_3, c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c27_3, c29_3, c_1 ---------------------------------------- (47) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c8(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0), ENCARG(and)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0), ENCARG(or)) ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0), ENCARG(forall)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0), ENCARG(forsome)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(and, x1)) -> c8(APP(and, encArg(x1)), ENCARG(and), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(APP(or, encArg(x1)), ENCARG(or), ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(APP(forall, encArg(x1)), ENCARG(forall), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(APP(forsome, encArg(x1)), ENCARG(forsome), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, and)) -> c8(APP(encArg(x0), and), ENCARG(x0), ENCARG(and)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, or)) -> c8(APP(encArg(x0), or), ENCARG(x0), ENCARG(or)) ENCARG(cons_app(x0, forall)) -> c8(APP(encArg(x0), forall), ENCARG(x0), ENCARG(forall)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c8(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, forsome)) -> c8(APP(encArg(x0), forsome), ENCARG(x0), ENCARG(forsome)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(and, x1)) -> c8(APP(and, encArg(x1)), ENCARG(and), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(APP(or, encArg(x1)), ENCARG(or), ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(APP(forall, encArg(x1)), ENCARG(forall), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(APP(forsome, encArg(x1)), ENCARG(forsome), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c27_3, c29_3, c_1, c8_3 ---------------------------------------- (49) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 29 trailing tuple parts ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c27_3, c29_3, c_1, c8_3, c8_1, c8_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, z0), app(app(cons, z1), z2)) -> c27(APP(app(and, app(z0, z1)), app(app(forall, z0), z2)), APP(z0, z1), APP(app(forall, z0), z2)) by APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c29_3, c_1, c8_3, c8_1, c8_2, c27_3 ---------------------------------------- (53) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, z0), app(app(cons, z1), z2)) -> c29(APP(app(or, app(z0, z1)), app(app(forsome, z0), z2)), APP(z0, z1), APP(app(forsome, z0), z2)) by APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c_1, c8_3, c8_1, c8_2, c27_3, c29_3 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by ENCODE_APP(x0, and) -> c(APP(encArg(x0), and)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, or) -> c(APP(encArg(x0), or)) ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(and, x1) -> c(APP(and, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(or, x1) -> c(APP(or, encArg(x1))) ENCODE_APP(forall, x1) -> c(APP(forall, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(forsome, x1) -> c(APP(forsome, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ---------------------------------------- (56) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, and) -> c(APP(encArg(x0), and)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, or) -> c(APP(encArg(x0), or)) ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(and, x1) -> c(APP(and, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(or, x1) -> c(APP(or, encArg(x1))) ENCODE_APP(forall, x1) -> c(APP(forall, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(forsome, x1) -> c(APP(forsome, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_3, c8_1, c8_2, c27_3, c29_3, c_1 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing nodes: ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(forsome, x1) -> c(APP(forsome, encArg(x1))) ENCODE_APP(x0, forall) -> c(APP(encArg(x0), forall)) ENCODE_APP(or, x1) -> c(APP(or, encArg(x1))) ENCODE_APP(forall, x1) -> c(APP(forall, encArg(x1))) ENCODE_APP(and, x1) -> c(APP(and, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(x0, forsome) -> c(APP(encArg(x0), forsome)) ENCODE_APP(x0, or) -> c(APP(encArg(x0), or)) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, and) -> c(APP(encArg(x0), and)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_3, c8_1, c8_2, c27_3, c29_3, c_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c8(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(APP(and, app(encArg(x1), encArg(x2))), ENCARG(and), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(APP(or, app(encArg(x1), encArg(x2))), ENCARG(or), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(APP(forall, app(encArg(x1), encArg(x2))), ENCARG(forall), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(APP(forsome, app(encArg(x1), encArg(x2))), ENCARG(forsome), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(APP(encArg(x0), app(and, encArg(x2))), ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(APP(encArg(x0), app(or, encArg(x2))), ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(APP(encArg(x0), app(forall, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(APP(encArg(x0), app(forsome, encArg(x2))), ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(APP(and, app(encArg(x1), encArg(x2))), ENCARG(and), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(APP(or, app(encArg(x1), encArg(x2))), ENCARG(or), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(APP(forall, app(encArg(x1), encArg(x2))), ENCARG(forall), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(APP(forsome, app(encArg(x1), encArg(x2))), ENCARG(forsome), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_3, c8_1, c8_2, c27_3, c29_3, c_1 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 24 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_3, c8_1, c8_2, c27_3, c29_3, c_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c8(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)), ENCARG(and)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)), ENCARG(or)) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)), ENCARG(forall)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)), ENCARG(forsome)) ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c8(APP(app(encArg(x0), encArg(x1)), app(encArg(z0), encArg(z1))), ENCARG(cons_app(x0, x1)), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(APP(app(encArg(x0), encArg(x1)), and), ENCARG(cons_app(x0, x1)), ENCARG(and)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(APP(app(encArg(x0), encArg(x1)), or), ENCARG(cons_app(x0, x1)), ENCARG(or)) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(APP(app(encArg(x0), encArg(x1)), forall), ENCARG(cons_app(x0, x1)), ENCARG(forall)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(APP(app(encArg(x0), encArg(x1)), forsome), ENCARG(cons_app(x0, x1)), ENCARG(forsome)) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c8_2, c27_3, c29_3, c_1, c8_3 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 17 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c8_2, c27_3, c29_3, c_1, c8_3 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, true)) -> c8(APP(encArg(x0), true), ENCARG(x0)) by ENCARG(cons_app(and, true)) -> c8(APP(and, true), ENCARG(and)) ENCARG(cons_app(true, true)) -> c8(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c8(APP(false, true), ENCARG(false)) ENCARG(cons_app(or, true)) -> c8(APP(or, true), ENCARG(or)) ENCARG(cons_app(forall, true)) -> c8(APP(forall, true), ENCARG(forall)) ENCARG(cons_app(nil, true)) -> c8(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c8(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(forsome, true)) -> c8(APP(forsome, true), ENCARG(forsome)) ENCARG(cons_app(cons_app(z0, z1), true)) -> c8(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(and, true)) -> c8(APP(and, true), ENCARG(and)) ENCARG(cons_app(true, true)) -> c8(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c8(APP(false, true), ENCARG(false)) ENCARG(cons_app(or, true)) -> c8(APP(or, true), ENCARG(or)) ENCARG(cons_app(forall, true)) -> c8(APP(forall, true), ENCARG(forall)) ENCARG(cons_app(nil, true)) -> c8(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c8(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(forsome, true)) -> c8(APP(forsome, true), ENCARG(forsome)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c8_2, c27_3, c29_3, c_1, c8_3 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing nodes: ENCARG(cons_app(and, true)) -> c8(APP(and, true), ENCARG(and)) ENCARG(cons_app(forall, true)) -> c8(APP(forall, true), ENCARG(forall)) ENCARG(cons_app(forsome, true)) -> c8(APP(forsome, true), ENCARG(forsome)) ENCARG(cons_app(or, true)) -> c8(APP(or, true), ENCARG(or)) ENCARG(cons_app(cons, true)) -> c8(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(false, true)) -> c8(APP(false, true), ENCARG(false)) ENCARG(cons_app(nil, true)) -> c8(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(true, true)) -> c8(APP(true, true), ENCARG(true)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c8_2, c27_3, c29_3, c_1, c8_3 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, false)) -> c8(APP(encArg(x0), false), ENCARG(x0)) by ENCARG(cons_app(and, false)) -> c8(APP(and, false), ENCARG(and)) ENCARG(cons_app(true, false)) -> c8(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c8(APP(false, false), ENCARG(false)) ENCARG(cons_app(or, false)) -> c8(APP(or, false), ENCARG(or)) ENCARG(cons_app(forall, false)) -> c8(APP(forall, false), ENCARG(forall)) ENCARG(cons_app(nil, false)) -> c8(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c8(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(forsome, false)) -> c8(APP(forsome, false), ENCARG(forsome)) ENCARG(cons_app(cons_app(z0, z1), false)) -> c8(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(and, false)) -> c8(APP(and, false), ENCARG(and)) ENCARG(cons_app(true, false)) -> c8(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c8(APP(false, false), ENCARG(false)) ENCARG(cons_app(or, false)) -> c8(APP(or, false), ENCARG(or)) ENCARG(cons_app(forall, false)) -> c8(APP(forall, false), ENCARG(forall)) ENCARG(cons_app(nil, false)) -> c8(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c8(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(forsome, false)) -> c8(APP(forsome, false), ENCARG(forsome)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c8_2, c27_3, c29_3, c_1, c8_3 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing nodes: ENCARG(cons_app(false, false)) -> c8(APP(false, false), ENCARG(false)) ENCARG(cons_app(cons, false)) -> c8(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(forsome, false)) -> c8(APP(forsome, false), ENCARG(forsome)) ENCARG(cons_app(or, false)) -> c8(APP(or, false), ENCARG(or)) ENCARG(cons_app(true, false)) -> c8(APP(true, false), ENCARG(true)) ENCARG(cons_app(nil, false)) -> c8(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(and, false)) -> c8(APP(and, false), ENCARG(and)) ENCARG(cons_app(forall, false)) -> c8(APP(forall, false), ENCARG(forall)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c8_2, c27_3, c29_3, c_1, c8_3 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c8(APP(encArg(x0), nil), ENCARG(x0)) by ENCARG(cons_app(and, nil)) -> c8(APP(and, nil), ENCARG(and)) ENCARG(cons_app(true, nil)) -> c8(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c8(APP(false, nil), ENCARG(false)) ENCARG(cons_app(or, nil)) -> c8(APP(or, nil), ENCARG(or)) ENCARG(cons_app(forall, nil)) -> c8(APP(forall, nil), ENCARG(forall)) ENCARG(cons_app(nil, nil)) -> c8(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c8(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(forsome, nil)) -> c8(APP(forsome, nil), ENCARG(forsome)) ENCARG(cons_app(cons_app(z0, z1), nil)) -> c8(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1))) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(and, nil)) -> c8(APP(and, nil), ENCARG(and)) ENCARG(cons_app(true, nil)) -> c8(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c8(APP(false, nil), ENCARG(false)) ENCARG(cons_app(or, nil)) -> c8(APP(or, nil), ENCARG(or)) ENCARG(cons_app(forall, nil)) -> c8(APP(forall, nil), ENCARG(forall)) ENCARG(cons_app(nil, nil)) -> c8(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c8(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(forsome, nil)) -> c8(APP(forsome, nil), ENCARG(forsome)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2 ---------------------------------------- (77) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing nodes: ENCARG(cons_app(forsome, nil)) -> c8(APP(forsome, nil), ENCARG(forsome)) ENCARG(cons_app(forall, nil)) -> c8(APP(forall, nil), ENCARG(forall)) ENCARG(cons_app(or, nil)) -> c8(APP(or, nil), ENCARG(or)) ENCARG(cons_app(cons, nil)) -> c8(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(false, nil)) -> c8(APP(false, nil), ENCARG(false)) ENCARG(cons_app(true, nil)) -> c8(APP(true, nil), ENCARG(true)) ENCARG(cons_app(and, nil)) -> c8(APP(and, nil), ENCARG(and)) ENCARG(cons_app(nil, nil)) -> c8(APP(nil, nil), ENCARG(nil)) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, z0), app(app(cons, x1), nil)) -> c27(APP(app(and, app(z0, x1)), true), APP(z0, x1), APP(app(forall, z0), nil)) by APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, true), false), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), true), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), false), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), true), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), false), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, false), true), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c27(APP(app(and, true), true), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c27(APP(app(and, false), true), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, true), false), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), true), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), false), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), true), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), false), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, false), true), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c27(APP(app(and, true), true), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c27(APP(app(and, false), true), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, true), false), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), true), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), false), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), true), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), false), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, false), true), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c27(APP(app(and, true), true), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c27(APP(app(and, false), true), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1 ---------------------------------------- (81) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2))), APP(z0, x1), APP(app(forall, z0), app(app(cons, z1), z2))) by APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(and, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(and, true)), x2)), APP(app(and, true), true), APP(app(forall, app(and, true)), x2)) by APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, z1), z2))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), z1)), app(app(forall, app(and, true)), z2))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(and, true), true), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2 ---------------------------------------- (87) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(and, true)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, true)), x2)), APP(app(and, true), false), APP(app(forall, app(and, true)), x2)) by APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, true), false), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, z1), z2))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), z1)), app(app(forall, app(and, true)), z2))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, z1), z2))) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, true), false), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, true), false), APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1 ---------------------------------------- (91) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(and, false)), app(app(cons, true), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), true), APP(app(forall, app(and, false)), x2)) by APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), true), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, z1), z2))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), z1)), app(app(forall, app(and, false)), z2))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, z1), z2))) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), true), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), true), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1 ---------------------------------------- (95) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(and, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(and, false)), x2)), APP(app(and, false), false), APP(app(forall, app(and, false)), x2)) by APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), false), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, z1), z2))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), z1)), app(app(forall, app(and, false)), z2))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, z1), z2))) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), false), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(and, false), false), APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1 ---------------------------------------- (99) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(or, true)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), true), APP(app(forall, app(or, true)), x2)) by APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), true), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, z1), z2))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), z1)), app(app(forall, app(or, true)), z2))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, z1), z2))) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), true), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), true), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1 ---------------------------------------- (103) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(or, true)), app(app(cons, false), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, true)), x2)), APP(app(or, true), false), APP(app(forall, app(or, true)), x2)) by APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), false), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, z1), z2))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), z1)), app(app(forall, app(or, true)), z2))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, z1), z2))) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), false), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c27(APP(app(and, true), true), APP(app(or, true), false), APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1 ---------------------------------------- (107) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(or, false)), app(app(cons, true), x2)) -> c27(APP(app(and, true), app(app(forall, app(or, false)), x2)), APP(app(or, false), true), APP(app(forall, app(or, false)), x2)) by APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, false), true), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, z1), z2))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), z1)), app(app(forall, app(or, false)), z2))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, z1), z2))) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, false), true), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c27(APP(app(and, true), true), APP(app(or, false), true), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1 ---------------------------------------- (111) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1 ---------------------------------------- (113) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(or, false)), app(app(cons, false), x2)) -> c27(APP(app(and, false), app(app(forall, app(or, false)), x2)), APP(app(or, false), false), APP(app(forall, app(or, false)), x2)) by APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, z1), z2))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), z1)), app(app(forall, app(or, false)), z2))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, z1), z2))) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c27(APP(app(and, false), true), APP(app(or, false), false), APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1 ---------------------------------------- (115) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, true), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), x2)) by APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c27(APP(app(and, true), true), APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), app(app(cons, z1), z2))) -> c27(APP(app(and, true), app(app(and, app(app(forall, x0), z1)), app(app(forall, app(forall, x0)), z2))), APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), app(app(cons, z1), z2))) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c27(APP(app(and, true), true), APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c27(APP(app(and, true), true), APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1 ---------------------------------------- (119) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), x2)) by APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c27(APP(app(and, app(app(and, app(x0, x1)), app(app(forall, x0), x2))), true), APP(app(forall, x0), app(app(cons, x1), x2)), APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c27(APP(app(and, app(app(and, app(x0, x1)), app(app(forall, x0), x2))), app(app(and, app(app(forall, x0), z1)), app(app(forall, app(forall, x0)), z2))), APP(app(forall, x0), app(app(cons, x1), x2)), APP(app(forall, app(forall, x0)), app(app(cons, z1), z2))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)) -> c27(APP(app(and, false), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), x2)) by APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c27(APP(app(and, false), true), APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), app(app(cons, z1), z2))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, x0), z1)), app(app(forall, app(forsome, x0)), z2))), APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), app(app(cons, z1), z2))) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c27(APP(app(and, false), true), APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c27(APP(app(and, false), true), APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1 ---------------------------------------- (125) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c27_3, c29_3, c_1, c8_3, c8_2, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), x2)) by APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c27(APP(app(and, app(app(or, app(x0, x1)), app(app(forsome, x0), x2))), true), APP(app(forsome, x0), app(app(cons, x1), x2)), APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c27(APP(app(and, app(app(or, app(x0, x1)), app(app(forsome, x0), x2))), app(app(and, app(app(forsome, x0), z1)), app(app(forall, app(forsome, x0)), z2))), APP(app(forsome, x0), app(app(cons, x1), x2)), APP(app(forall, app(forsome, x0)), app(app(cons, z1), z2))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1 ---------------------------------------- (129) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, z0), app(app(cons, x1), nil)) -> c29(APP(app(or, app(z0, x1)), false), APP(z0, x1), APP(app(forsome, z0), nil)) by APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, true), false), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), true), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), false), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), true), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), false), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, false), true), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c29(APP(app(or, true), false), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c29(APP(app(or, false), false), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, true), false), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), true), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), false), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), true), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), false), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, false), true), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c29(APP(app(or, true), false), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c29(APP(app(or, false), false), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, true), false), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), true), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), false), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), true), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), false), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, false), true), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c29(APP(app(or, true), false), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c29(APP(app(or, false), false), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1 ---------------------------------------- (131) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1 ---------------------------------------- (133) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, z1), z2))) by APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(and, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(and, true)), x2)), APP(app(and, true), true), APP(app(forsome, app(and, true)), x2)) by APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, z1), z2))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), z1)), app(app(forsome, app(and, true)), z2))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(and, true), true), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2 ---------------------------------------- (137) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(and, true)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, true)), x2)), APP(app(and, true), false), APP(app(forsome, app(and, true)), x2)) by APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, true), false), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, z1), z2))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), z1)), app(app(forsome, app(and, true)), z2))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, z1), z2))) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, true), false), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, true), false), APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1 ---------------------------------------- (141) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(and, false)), app(app(cons, true), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), true), APP(app(forsome, app(and, false)), x2)) by APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), true), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, z1), z2))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), z1)), app(app(forsome, app(and, false)), z2))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, z1), z2))) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), true), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), true), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1 ---------------------------------------- (145) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(and, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(and, false)), x2)), APP(app(and, false), false), APP(app(forsome, app(and, false)), x2)) by APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), false), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, z1), z2))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), z1)), app(app(forsome, app(and, false)), z2))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, z1), z2))) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), false), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(and, false), false), APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1 ---------------------------------------- (149) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(or, true)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), true), APP(app(forsome, app(or, true)), x2)) by APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), true), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, z1), z2))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), z1)), app(app(forsome, app(or, true)), z2))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, z1), z2))) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), true), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), true), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1 ---------------------------------------- (153) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(or, true)), app(app(cons, false), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, true)), x2)), APP(app(or, true), false), APP(app(forsome, app(or, true)), x2)) by APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), false), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, z1), z2))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), z1)), app(app(forsome, app(or, true)), z2))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, z1), z2))) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), false), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c29(APP(app(or, true), false), APP(app(or, true), false), APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1 ---------------------------------------- (157) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(or, false)), app(app(cons, true), x2)) -> c29(APP(app(or, true), app(app(forsome, app(or, false)), x2)), APP(app(or, false), true), APP(app(forsome, app(or, false)), x2)) by APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, false), true), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, z1), z2))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), z1)), app(app(forsome, app(or, false)), z2))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, z1), z2))) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, false), true), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c29(APP(app(or, true), false), APP(app(or, false), true), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1 ---------------------------------------- (161) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(or, false)), app(app(cons, false), x2)) -> c29(APP(app(or, false), app(app(forsome, app(or, false)), x2)), APP(app(or, false), false), APP(app(forsome, app(or, false)), x2)) by APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, z1), z2))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), z1)), app(app(forsome, app(or, false)), z2))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, z1), z2))) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c29(APP(app(or, false), false), APP(app(or, false), false), APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1 ---------------------------------------- (165) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, true), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), x2)) by APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c29(APP(app(or, true), false), APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), app(app(cons, z1), z2))) -> c29(APP(app(or, true), app(app(or, app(app(forall, x0), z1)), app(app(forsome, app(forall, x0)), z2))), APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), app(app(cons, z1), z2))) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c29(APP(app(or, true), false), APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c29(APP(app(or, true), false), APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1 ---------------------------------------- (169) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2)), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), x2)) by APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c29(APP(app(or, app(app(and, app(x0, x1)), app(app(forall, x0), x2))), false), APP(app(forall, x0), app(app(cons, x1), x2)), APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c29(APP(app(or, app(app(and, app(x0, x1)), app(app(forall, x0), x2))), app(app(or, app(app(forall, x0), z1)), app(app(forsome, app(forall, x0)), z2))), APP(app(forall, x0), app(app(cons, x1), x2)), APP(app(forsome, app(forall, x0)), app(app(cons, z1), z2))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1 ---------------------------------------- (173) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)) -> c29(APP(app(or, false), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), x2)) by APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c29(APP(app(or, false), false), APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), app(app(cons, z1), z2))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, x0), z1)), app(app(forsome, app(forsome, x0)), z2))), APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), app(app(cons, z1), z2))) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c29(APP(app(or, false), false), APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c29(APP(app(or, false), false), APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1 ---------------------------------------- (175) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c29_3, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1 ---------------------------------------- (177) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2)), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), x2)) by APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), nil)) -> c29(APP(app(or, app(app(or, app(x0, x1)), app(app(forsome, x0), x2))), false), APP(app(forsome, x0), app(app(cons, x1), x2)), APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), app(app(cons, z1), z2))) -> c29(APP(app(or, app(app(or, app(x0, x1)), app(app(forsome, x0), x2))), app(app(or, app(app(forsome, x0), z1)), app(app(forsome, app(forsome, x0)), z2))), APP(app(forsome, x0), app(app(cons, x1), x2)), APP(app(forsome, app(forsome, x0)), app(app(cons, z1), z2))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_3, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) by ENCODE_APP(and, true) -> c(APP(and, true)) ENCODE_APP(true, true) -> c(APP(true, true)) ENCODE_APP(false, true) -> c(APP(false, true)) ENCODE_APP(or, true) -> c(APP(or, true)) ENCODE_APP(forall, true) -> c(APP(forall, true)) ENCODE_APP(nil, true) -> c(APP(nil, true)) ENCODE_APP(cons, true) -> c(APP(cons, true)) ENCODE_APP(forsome, true) -> c(APP(forsome, true)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) ENCODE_APP(and, true) -> c(APP(and, true)) ENCODE_APP(true, true) -> c(APP(true, true)) ENCODE_APP(false, true) -> c(APP(false, true)) ENCODE_APP(or, true) -> c(APP(or, true)) ENCODE_APP(forall, true) -> c(APP(forall, true)) ENCODE_APP(nil, true) -> c(APP(nil, true)) ENCODE_APP(cons, true) -> c(APP(cons, true)) ENCODE_APP(forsome, true) -> c(APP(forsome, true)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_3, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing nodes: ENCODE_APP(true, true) -> c(APP(true, true)) ENCODE_APP(and, true) -> c(APP(and, true)) ENCODE_APP(forall, true) -> c(APP(forall, true)) ENCODE_APP(forsome, true) -> c(APP(forsome, true)) ENCODE_APP(or, true) -> c(APP(or, true)) ENCODE_APP(cons, true) -> c(APP(cons, true)) ENCODE_APP(false, true) -> c(APP(false, true)) ENCODE_APP(nil, true) -> c(APP(nil, true)) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_3, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) by ENCODE_APP(and, false) -> c(APP(and, false)) ENCODE_APP(true, false) -> c(APP(true, false)) ENCODE_APP(false, false) -> c(APP(false, false)) ENCODE_APP(or, false) -> c(APP(or, false)) ENCODE_APP(forall, false) -> c(APP(forall, false)) ENCODE_APP(nil, false) -> c(APP(nil, false)) ENCODE_APP(cons, false) -> c(APP(cons, false)) ENCODE_APP(forsome, false) -> c(APP(forsome, false)) ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false)) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) ENCODE_APP(and, false) -> c(APP(and, false)) ENCODE_APP(true, false) -> c(APP(true, false)) ENCODE_APP(false, false) -> c(APP(false, false)) ENCODE_APP(or, false) -> c(APP(or, false)) ENCODE_APP(forall, false) -> c(APP(forall, false)) ENCODE_APP(nil, false) -> c(APP(nil, false)) ENCODE_APP(cons, false) -> c(APP(cons, false)) ENCODE_APP(forsome, false) -> c(APP(forsome, false)) ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_3, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1 ---------------------------------------- (185) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing nodes: ENCODE_APP(and, false) -> c(APP(and, false)) ENCODE_APP(nil, false) -> c(APP(nil, false)) ENCODE_APP(forall, false) -> c(APP(forall, false)) ENCODE_APP(cons, false) -> c(APP(cons, false)) ENCODE_APP(false, false) -> c(APP(false, false)) ENCODE_APP(true, false) -> c(APP(true, false)) ENCODE_APP(forsome, false) -> c(APP(forsome, false)) ENCODE_APP(or, false) -> c(APP(or, false)) ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: encArg(and) -> and encArg(true) -> true encArg(false) -> false encArg(or) -> or encArg(forall) -> forall encArg(nil) -> nil encArg(cons) -> cons encArg(forsome) -> forsome encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(and, true), true) -> true app(app(and, true), false) -> false app(app(and, false), true) -> false app(app(and, false), false) -> false app(app(or, true), true) -> true app(app(or, true), false) -> true app(app(or, false), true) -> true app(app(or, false), false) -> false app(app(forall, z0), nil) -> true app(app(forall, z0), app(app(cons, z1), z2)) -> app(app(and, app(z0, z1)), app(app(forall, z0), z2)) app(app(forsome, z0), nil) -> false app(app(forsome, z0), app(app(cons, z1), z2)) -> app(app(or, app(z0, z1)), app(app(forsome, z0), z2)) Tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 ENCARG(cons_app(x0, and)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, or)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forall)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c8(ENCARG(x0)) ENCARG(cons_app(x0, forsome)) -> c8(ENCARG(x0)) ENCARG(cons_app(and, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(or, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forall, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c8(ENCARG(x1)) ENCARG(cons_app(forsome, x1)) -> c8(ENCARG(x1)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, and))) -> c8(APP(encArg(x0), app(encArg(x1), and)), ENCARG(x0), ENCARG(cons_app(x1, and))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c8(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c8(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, or))) -> c8(APP(encArg(x0), app(encArg(x1), or)), ENCARG(x0), ENCARG(cons_app(x1, or))) ENCARG(cons_app(x0, cons_app(x1, forall))) -> c8(APP(encArg(x0), app(encArg(x1), forall)), ENCARG(x0), ENCARG(cons_app(x1, forall))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c8(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c8(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, forsome))) -> c8(APP(encArg(x0), app(encArg(x1), forsome)), ENCARG(x0), ENCARG(cons_app(x1, forsome))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c8(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1)))), ENCARG(x0), ENCARG(cons_app(x1, cons_app(z0, z1)))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c8(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons_app(z0, z1), x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c8(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(x0, cons_app(and, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(and, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(or, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(or, x2))) ENCARG(cons_app(x0, cons_app(forall, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forall, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(forsome, x2))) -> c8(ENCARG(x0), ENCARG(cons_app(forsome, x2))) ENCARG(cons_app(and, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(or, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forall, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(forsome, cons_app(x1, x2))) -> c8(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, and), x2)) -> c8(APP(app(encArg(x0), and), encArg(x2)), ENCARG(cons_app(x0, and)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c8(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c8(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, or), x2)) -> c8(APP(app(encArg(x0), or), encArg(x2)), ENCARG(cons_app(x0, or)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forall), x2)) -> c8(APP(app(encArg(x0), forall), encArg(x2)), ENCARG(cons_app(x0, forall)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c8(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c8(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, forsome), x2)) -> c8(APP(app(encArg(x0), forsome), encArg(x2)), ENCARG(cons_app(x0, forsome)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c8(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2)), ENCARG(cons_app(x0, cons_app(z0, z1))), ENCARG(x2)) ENCARG(cons_app(cons_app(and, x1), x2)) -> c8(APP(app(and, encArg(x1)), encArg(x2)), ENCARG(cons_app(and, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(or, x1), x2)) -> c8(APP(app(or, encArg(x1)), encArg(x2)), ENCARG(cons_app(or, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forall, x1), x2)) -> c8(APP(app(forall, encArg(x1)), encArg(x2)), ENCARG(cons_app(forall, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(forsome, x1), x2)) -> c8(APP(app(forsome, encArg(x1)), encArg(x2)), ENCARG(cons_app(forsome, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c8(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2)), ENCARG(cons_app(cons_app(z0, z1), x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, x1), and)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c8(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c8(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), or)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forall)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c8(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), forsome)) -> c8(ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(true, x1), x2)) -> c8(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c8(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c8(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c8(ENCARG(cons_app(cons, x1)), ENCARG(x2)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false)) S tuples: APP(app(and, true), true) -> c18 APP(app(and, true), false) -> c19 APP(app(and, false), true) -> c20 APP(app(and, false), false) -> c21 APP(app(or, true), true) -> c22 APP(app(or, true), false) -> c23 APP(app(or, false), true) -> c24 APP(app(or, false), false) -> c25 APP(app(forall, z0), nil) -> c26 APP(app(forsome, z0), nil) -> c28 APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), true), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), true), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, x0), app(app(cons, x1), nil)) -> c27(APP(app(forall, x0), nil)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c1(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, true), true)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, z0), nil)) APP(app(forall, app(forall, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forall, z0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(and, false), true)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forsome, z0), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, nil), nil)) -> c1(APP(app(forall, app(forsome, z0)), nil)) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), true)), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), nil))) APP(app(forall, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c27(APP(app(and, app(z0, x1)), app(app(and, app(z0, x2)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), APP(z0, x1), APP(app(forall, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, true), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, true), x3))) APP(app(forall, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, true), x1)), app(app(and, false), app(app(forall, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forall, app(and, true)), app(app(cons, false), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, true), x3))) APP(app(forall, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(and, false), x1)), app(app(and, false), app(app(forall, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forall, app(and, false)), app(app(cons, false), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, true), x3))) APP(app(forall, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, true), x1)), app(app(and, true), app(app(forall, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forall, app(or, true)), app(app(cons, false), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, true), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, true), x3))) APP(app(forall, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c27(APP(app(and, app(app(or, false), x1)), app(app(and, false), app(app(forall, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forall, app(or, false)), app(app(cons, false), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, true), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forall, z0), x1)), app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, false), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c27(APP(app(and, app(app(forsome, z0), x1)), app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forall, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), true), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, true), x2)), app(app(forall, app(and, true)), x3))), APP(app(and, true), false), APP(app(forall, app(and, true)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), true), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(and, false), x2)), app(app(forall, app(and, false)), x3))), APP(app(and, false), false), APP(app(forall, app(and, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), true), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, true), x2)), app(app(forall, app(or, true)), x3))), APP(app(or, true), false), APP(app(forall, app(or, true)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), true), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(or, false), x2)), app(app(forall, app(or, false)), x3))), APP(app(or, false), false), APP(app(forall, app(or, false)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, true), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(and, app(app(forall, z0), x2)), app(app(forall, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forall, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c27(APP(app(and, false), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c27(APP(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(and, app(app(forsome, z0), x2)), app(app(forall, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forall, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forall, app(and, true)), app(app(cons, true), x0)) -> c27(APP(app(and, true), true), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(and, true), true)) APP(app(forall, app(and, true)), app(app(cons, true), nil)) -> c2(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, true)), app(app(cons, false), x0)) -> c27(APP(app(and, true), false), APP(app(forall, app(and, true)), x0)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, false), true)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(and, true), false)) APP(app(forall, app(and, true)), app(app(cons, false), nil)) -> c3(APP(app(forall, app(and, true)), nil)) APP(app(forall, app(and, false)), app(app(cons, true), x0)) -> c27(APP(app(and, false), true), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, true), nil)) -> c4(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(and, false)), app(app(cons, false), x0)) -> c27(APP(app(and, false), false), APP(app(forall, app(and, false)), x0)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), true)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(and, false), false)) APP(app(forall, app(and, false)), app(app(cons, false), nil)) -> c5(APP(app(forall, app(and, false)), nil)) APP(app(forall, app(or, true)), app(app(cons, true), x0)) -> c27(APP(app(or, true), true), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(or, true), true)) APP(app(forall, app(or, true)), app(app(cons, true), nil)) -> c6(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, true)), app(app(cons, false), x0)) -> c27(APP(app(or, true), false), APP(app(forall, app(or, true)), x0)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(and, true), true)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(or, true), false)) APP(app(forall, app(or, true)), app(app(cons, false), nil)) -> c7(APP(app(forall, app(or, true)), nil)) APP(app(forall, app(or, false)), app(app(cons, true), x0)) -> c27(APP(app(or, false), true), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(and, true), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(or, false), true)) APP(app(forall, app(or, false)), app(app(cons, true), nil)) -> c9(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(or, false)), app(app(cons, false), x0)) -> c27(APP(app(or, false), false), APP(app(forall, app(or, false)), x0)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(and, false), true)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(or, false), false)) APP(app(forall, app(or, false)), app(app(cons, false), nil)) -> c10(APP(app(forall, app(or, false)), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forall, x0), nil), APP(app(forall, app(forall, x0)), x1)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(and, true), true)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, x0), nil)) APP(app(forall, app(forall, x0)), app(app(cons, nil), nil)) -> c11(APP(app(forall, app(forall, x0)), nil)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), true)), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forall, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forall, z0)), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forall, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, true))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forall, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(and, false))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forall, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, true))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forall, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forall, app(or, false))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forall, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forall, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forall, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forall, app(forsome, z0))), x3)) APP(app(forall, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forall, x0)), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), x1)) -> c27(APP(app(forsome, x0), nil), APP(app(forall, app(forsome, x0)), x1)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(and, false), true)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forsome, x0), nil)) APP(app(forall, app(forsome, x0)), app(app(cons, nil), nil)) -> c12(APP(app(forall, app(forsome, x0)), nil)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), false)), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c27(APP(app(and, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forall, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forall, app(forsome, z0)), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forall, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, true))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forall, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(or, false))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forall, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, true))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forall, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forall, app(forsome, app(and, false))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forall, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forall, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c27(APP(app(and, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c27(APP(app(and, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forall, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forall, app(forsome, app(forsome, z0))), x3)) APP(app(forall, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c27(APP(app(forall, app(forsome, x0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), false), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), nil)) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), false), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, x0), app(app(cons, x1), nil)) -> c29(APP(app(forsome, x0), nil)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c13(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, true), false)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forall, z0), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forall, z0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(or, false), false)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, z0), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), nil)) -> c13(APP(app(forsome, app(forsome, z0)), nil)) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), nil))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), false)), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), nil))) APP(app(forsome, z0), app(app(cons, x1), app(app(cons, x2), app(app(cons, z1), z2)))) -> c29(APP(app(or, app(z0, x1)), app(app(or, app(z0, x2)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), APP(z0, x1), APP(app(forsome, z0), app(app(cons, x2), app(app(cons, z1), z2)))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, true), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, true), x3))) APP(app(forsome, app(and, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, true), x1)), app(app(or, false), app(app(forsome, app(and, true)), x3))), APP(app(and, true), x1), APP(app(forsome, app(and, true)), app(app(cons, false), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, true), x3))) APP(app(forsome, app(and, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(and, false), x1)), app(app(or, false), app(app(forsome, app(and, false)), x3))), APP(app(and, false), x1), APP(app(forsome, app(and, false)), app(app(cons, false), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, true), x3))) APP(app(forsome, app(or, true)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, true), x1)), app(app(or, true), app(app(forsome, app(or, true)), x3))), APP(app(or, true), x1), APP(app(forsome, app(or, true)), app(app(cons, false), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, true), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, true), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, true), x3))) APP(app(forsome, app(or, false)), app(app(cons, x1), app(app(cons, false), x3))) -> c29(APP(app(or, app(app(or, false), x1)), app(app(or, false), app(app(forsome, app(or, false)), x3))), APP(app(or, false), x1), APP(app(forsome, app(or, false)), app(app(cons, false), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, true), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forall, z0), x1)), app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), x1), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, nil), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, false), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, x1), app(app(cons, app(app(cons, z1), z2)), x3))) -> c29(APP(app(or, app(app(forsome, z0), x1)), app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), x1), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), true), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, true), x2)), app(app(forsome, app(and, true)), x3))), APP(app(and, true), false), APP(app(forsome, app(and, true)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), true), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(and, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(and, false), x2)), app(app(forsome, app(and, false)), x3))), APP(app(and, false), false), APP(app(forsome, app(and, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), true), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, true)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, true), x2)), app(app(forsome, app(or, true)), x3))), APP(app(or, true), false), APP(app(forsome, app(or, true)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, true), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), true), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(or, false)), app(app(cons, false), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(or, false), x2)), app(app(forsome, app(or, false)), x3))), APP(app(or, false), false), APP(app(forsome, app(or, false)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, true), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), nil), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(or, app(app(forall, z0), x2)), app(app(forsome, app(forall, z0)), x3))), APP(app(forall, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forall, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, nil), app(app(cons, x2), x3))) -> c29(APP(app(or, false), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), nil), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), app(app(cons, x2), x3))) -> c29(APP(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(or, app(app(forsome, z0), x2)), app(app(forsome, app(forsome, z0)), x3))), APP(app(forsome, z0), app(app(cons, z1), z2)), APP(app(forsome, app(forsome, z0)), app(app(cons, x2), x3))) APP(app(forsome, app(and, true)), app(app(cons, true), x0)) -> c29(APP(app(and, true), true), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(or, true), false)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(and, true), true)) APP(app(forsome, app(and, true)), app(app(cons, true), nil)) -> c14(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, true)), app(app(cons, false), x0)) -> c29(APP(app(and, true), false), APP(app(forsome, app(and, true)), x0)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(or, false), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(and, true), false)) APP(app(forsome, app(and, true)), app(app(cons, false), nil)) -> c15(APP(app(forsome, app(and, true)), nil)) APP(app(forsome, app(and, false)), app(app(cons, true), x0)) -> c29(APP(app(and, false), true), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(and, false), true)) APP(app(forsome, app(and, false)), app(app(cons, true), nil)) -> c16(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(and, false)), app(app(cons, false), x0)) -> c29(APP(app(and, false), false), APP(app(forsome, app(and, false)), x0)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(or, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(and, false), false)) APP(app(forsome, app(and, false)), app(app(cons, false), nil)) -> c17(APP(app(forsome, app(and, false)), nil)) APP(app(forsome, app(or, true)), app(app(cons, true), x0)) -> c29(APP(app(or, true), true), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(or, true), true)) APP(app(forsome, app(or, true)), app(app(cons, true), nil)) -> c30(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, true)), app(app(cons, false), x0)) -> c29(APP(app(or, true), false), APP(app(forsome, app(or, true)), x0)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(or, true), false)) APP(app(forsome, app(or, true)), app(app(cons, false), nil)) -> c31(APP(app(forsome, app(or, true)), nil)) APP(app(forsome, app(or, false)), app(app(cons, true), x0)) -> c29(APP(app(or, false), true), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, true), false)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(or, false), true)) APP(app(forsome, app(or, false)), app(app(cons, true), nil)) -> c32(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(or, false)), app(app(cons, false), x0)) -> c29(APP(app(or, false), false), APP(app(forsome, app(or, false)), x0)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(or, false), false)) APP(app(forsome, app(or, false)), app(app(cons, false), nil)) -> c33(APP(app(forsome, app(or, false)), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forall, x0), nil), APP(app(forsome, app(forall, x0)), x1)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(or, true), false)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forall, x0), nil)) APP(app(forsome, app(forall, x0)), app(app(cons, nil), nil)) -> c34(APP(app(forsome, app(forall, x0)), nil)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), true)), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(and, app(z0, x1)), app(app(and, app(z0, z1)), app(app(forall, z0), z2)))), app(app(forsome, app(forall, z0)), x3)), APP(app(forall, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forall, z0)), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, true)), x2))), app(app(forsome, app(forall, app(and, true))), x3)), APP(app(forall, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, true))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(and, false)), x2))), app(app(forsome, app(forall, app(and, false))), x3)), APP(app(forall, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(and, false))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, true)), x2))), app(app(forsome, app(forall, app(or, true))), x3)), APP(app(forall, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, true))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(or, false)), x2))), app(app(forsome, app(forall, app(or, false))), x3)), APP(app(forall, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forall, app(or, false))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, true), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forall, app(forall, z0)), x2))), app(app(forsome, app(forall, app(forall, z0))), x3)), APP(app(forall, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forall, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(and, false), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(and, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forall, app(forsome, z0)), x2))), app(app(forsome, app(forall, app(forsome, z0))), x3)), APP(app(forall, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forall, app(forsome, z0))), x3)) APP(app(forsome, app(forall, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forall, x0)), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), x1)) -> c29(APP(app(forsome, x0), nil), APP(app(forsome, app(forsome, x0)), x1)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(or, false), false)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, x0), nil)) APP(app(forsome, app(forsome, x0)), app(app(cons, nil), nil)) -> c35(APP(app(forsome, app(forsome, x0)), nil)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), nil)), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), false)), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), nil)), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, x1), app(app(cons, z1), z2))), x3)) -> c29(APP(app(or, app(app(or, app(z0, x1)), app(app(or, app(z0, z1)), app(app(forsome, z0), z2)))), app(app(forsome, app(forsome, z0)), x3)), APP(app(forsome, z0), app(app(cons, x1), app(app(cons, z1), z2))), APP(app(forsome, app(forsome, z0)), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, true)), x2))), app(app(forsome, app(forsome, app(or, true))), x3)), APP(app(forsome, app(or, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, true))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(or, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(or, false)), x2))), app(app(forsome, app(forsome, app(or, false))), x3)), APP(app(forsome, app(or, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(or, false))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, true))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, true)), x2))), app(app(forsome, app(forsome, app(and, true))), x3)), APP(app(forsome, app(and, true)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, true))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, true), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, true), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(and, false))), app(app(cons, app(app(cons, false), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(and, false)), x2))), app(app(forsome, app(forsome, app(and, false))), x3)), APP(app(forsome, app(and, false)), app(app(cons, false), x2)), APP(app(forsome, app(forsome, app(and, false))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, true), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forall, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(and, app(z0, z1)), app(app(forall, z0), z2))), app(app(forsome, app(forall, z0)), x2))), app(app(forsome, app(forsome, app(forall, z0))), x3)), APP(app(forsome, app(forall, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forall, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c29(APP(app(or, app(app(or, false), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, nil), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, app(forsome, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c29(APP(app(or, app(app(or, app(app(or, app(z0, z1)), app(app(forsome, z0), z2))), app(app(forsome, app(forsome, z0)), x2))), app(app(forsome, app(forsome, app(forsome, z0))), x3)), APP(app(forsome, app(forsome, z0)), app(app(cons, app(app(cons, z1), z2)), x2)), APP(app(forsome, app(forsome, app(forsome, z0))), x3)) APP(app(forsome, app(forsome, x0)), app(app(cons, app(app(cons, x1), x2)), x3)) -> c29(APP(app(forsome, app(forsome, x0)), x3)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c18, c19, c20, c21, c22, c23, c24, c25, c26, c28, c8_1, c_1, c8_3, c8_2, c27_3, c27_1, c1_1, c27_2, c2_1, c3_1, c4_1, c5_1, c6_1, c7_1, c9_1, c10_1, c11_1, c12_1, c29_3, c29_1, c13_1, c29_2, c14_1, c15_1, c16_1, c17_1, c30_1, c31_1, c32_1, c33_1, c34_1, c35_1