/export/starexec/sandbox/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- KILLED proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, INF).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), 219 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (14) CpxTRS (15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (16) CpxRelTRS (17) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxWeightedTrs (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CpxTypedWeightedTrs (21) CompletionProof [UPPER BOUND(ID), 0 ms] (22) CpxTypedWeightedCompleteTrs (23) NarrowingProof [BOTH BOUNDS(ID, ID), 41 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 23 ms] (26) CpxRNTS (27) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxRNTS (29) CompletionProof [UPPER BOUND(ID), 0 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 8 ms] (32) CpxRNTS (33) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (34) CdtProblem (35) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CdtProblem (37) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (38) CdtProblem (39) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (42) CdtProblem (43) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CdtProblem (45) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms] (46) CdtProblem (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CdtProblem (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CdtProblem (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (52) CdtProblem (53) CdtRhsSimplificationProcessorProof [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), 49 ms] (60) CdtProblem (61) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 16 ms] (62) CdtProblem (63) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 82 ms] (64) CdtProblem (65) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 44 ms] (66) CdtProblem (67) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 21 ms] (72) CdtProblem (73) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (76) CdtProblem (77) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (80) CdtProblem (81) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (84) CdtProblem (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (90) CdtProblem (91) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (94) CdtProblem (95) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (98) CdtProblem (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6 ms] (102) CdtProblem (103) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (106) CdtProblem (107) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (116) CdtProblem (117) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (118) CdtProblem (119) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (122) CdtProblem (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (124) CdtProblem (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (126) CdtProblem (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2 ms] (136) CdtProblem (137) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (138) CdtProblem (139) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (140) CdtProblem (141) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (144) CdtProblem (145) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (152) CdtProblem (153) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (154) CdtProblem (155) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (162) CdtProblem (163) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 23 ms] (164) CdtProblem (165) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (166) CdtProblem (167) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (168) CdtProblem (169) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (170) CdtProblem (171) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 34 ms] (172) CdtProblem (173) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms] (176) CdtProblem (177) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 40 ms] (180) CdtProblem (181) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 6357 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [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(., 1), x) -> x app(app(., x), 1) -> x app(app(., app(i, x)), x) -> 1 app(app(., x), app(i, x)) -> 1 app(app(., app(i, y)), app(app(., y), z)) -> z app(app(., y), app(app(., app(i, y)), z)) -> z app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(i, 1) -> 1 app(i, app(i, x)) -> x app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), 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(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false ---------------------------------------- (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(., 1), x) -> x app(app(., x), 1) -> x app(app(., app(i, x)), x) -> 1 app(app(., x), app(i, x)) -> 1 app(app(., app(i, y)), app(app(., y), z)) -> z app(app(., y), app(app(., app(i, y)), z)) -> z app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(i, 1) -> 1 app(i, app(i, x)) -> x app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false 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(., 1), x) -> x app(app(., x), 1) -> x app(app(., app(i, x)), x) -> 1 app(app(., x), app(i, x)) -> 1 app(app(., app(i, y)), app(app(., y), z)) -> z app(app(., y), app(app(., app(i, y)), z)) -> z app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(i, 1) -> 1 app(i, app(i, x)) -> x app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false Rewrite Strategy: INNERMOST ---------------------------------------- (5) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (6) 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(., 1'), x) -> x app(app(., x), 1') -> x app(app(., app(i, x)), x) -> 1' app(app(., x), app(i, x)) -> 1' app(app(., app(i, y)), app(app(., y), z)) -> z app(app(., y), app(app(., app(i, y)), z)) -> z app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(i, 1') -> 1' app(i, app(i, x)) -> x app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(.) -> . encArg(1') -> 1' encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1' encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false Rewrite Strategy: INNERMOST ---------------------------------------- (7) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (8) Obligation: Innermost TRS: Rules: app(app(., 1'), x) -> x app(app(., x), 1') -> x app(app(., app(i, x)), x) -> 1' app(app(., x), app(i, x)) -> 1' app(app(., app(i, y)), app(app(., y), z)) -> z app(app(., y), app(app(., app(i, y)), z)) -> z app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(i, 1') -> 1' app(i, app(i, x)) -> x app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(.) -> . encArg(1') -> 1' encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1' encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false Types: app :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app . :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app 1' :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app i :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app map :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app nil :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app cons :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app filter :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app filter2 :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app true :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app false :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encArg :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app cons_app :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_app :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_. :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_1 :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_i :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_map :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_nil :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_cons :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_filter :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_filter2 :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_true :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_false :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app hole_.:1':i:map:nil:cons:filter:filter2:true:false:cons_app1_0 :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app gen_.:1':i:map:nil:cons:filter:filter2:true:false:cons_app2_0 :: Nat -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app ---------------------------------------- (9) 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 ---------------------------------------- (10) Obligation: Innermost TRS: Rules: app(app(., 1'), x) -> x app(app(., x), 1') -> x app(app(., app(i, x)), x) -> 1' app(app(., x), app(i, x)) -> 1' app(app(., app(i, y)), app(app(., y), z)) -> z app(app(., y), app(app(., app(i, y)), z)) -> z app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(i, 1') -> 1' app(i, app(i, x)) -> x app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(.) -> . encArg(1') -> 1' encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1' encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false Types: app :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app . :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app 1' :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app i :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app map :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app nil :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app cons :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app filter :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app filter2 :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app true :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app false :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encArg :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app cons_app :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_app :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_. :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_1 :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_i :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_map :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_nil :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_cons :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_filter :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_filter2 :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_true :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app encode_false :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app hole_.:1':i:map:nil:cons:filter:filter2:true:false:cons_app1_0 :: .:1':i:map:nil:cons:filter:filter2:true:false:cons_app gen_.:1':i:map:nil:cons:filter:filter2:true:false:cons_app2_0 :: Nat -> .:1':i:map:nil:cons:filter:filter2:true:false:cons_app Generator Equations: gen_.:1':i:map:nil:cons:filter:filter2:true:false:cons_app2_0(0) <=> . gen_.:1':i:map:nil:cons:filter:filter2:true:false:cons_app2_0(+(x, 1)) <=> cons_app(., gen_.:1':i:map:nil:cons:filter:filter2:true:false: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 ---------------------------------------- (11) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (12) 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(., 1), x) -> x app(app(., x), 1) -> x app(app(., app(i, x)), x) -> 1 app(app(., x), app(i, x)) -> 1 app(app(., app(i, y)), app(app(., y), z)) -> z app(app(., y), app(app(., app(i, y)), z)) -> z app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(i, 1) -> 1 app(i, app(i, x)) -> x app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) The (relative) TRS S consists of the following rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false Rewrite Strategy: INNERMOST ---------------------------------------- (13) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (14) 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(., 1), x) -> x app(app(., x), 1) -> x app(app(., app(i, x)), x) -> 1 app(app(., x), app(i, x)) -> 1 app(app(., app(i, y)), app(app(., y), z)) -> z app(app(., y), app(app(., app(i, y)), z)) -> z app(app(., app(app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(i, 1) -> 1 app(i, app(i, x)) -> x app(i, app(app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(app(map, f), nil) -> nil app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(app(filter, f), nil) -> nil app(app(filter, f), app(app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(app(app(app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(app(app(app(filter2, false), f), x), xs) -> app(app(filter, f), xs) encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (15) NonCtorToCtorProof (UPPER BOUND(ID)) transformed non-ctor to ctor-system ---------------------------------------- (16) 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(i, 1) -> 1 app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) app(i, c_app(i, x)) -> x app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) app(c_app(., c_app(i, x)), x) -> 1 app(c_app(map, f), nil) -> nil app(c_app(filter, f), nil) -> nil app(c_app(., 1), x) -> x app(c_app(., x), 1) -> x app(c_app(., c_app(c_app(., x), y)), z) -> app(app(., x), app(app(., y), z)) app(c_app(., c_app(i, y)), c_app(c_app(., y), z)) -> z app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) app(c_app(., x), c_app(i, x)) -> 1 app(i, c_app(c_app(., x), y)) -> app(app(., app(i, y)), app(i, x)) app(c_app(., y), c_app(c_app(., c_app(i, y)), z)) -> z The (relative) TRS S consists of the following rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false 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_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(x0, x1) -> c_app(x0, x1) Rewrite Strategy: INNERMOST ---------------------------------------- (17) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (18) 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(i, 1) -> 1 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(i, c_app(i, x)) -> x [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(., c_app(i, x)), x) -> 1 [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(., 1), x) -> x [1] app(c_app(., x), 1) -> x [1] app(c_app(., c_app(c_app(., x), y)), z) -> app(app(., x), app(app(., y), z)) [1] app(c_app(., c_app(i, y)), c_app(c_app(., y), z)) -> z [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(., x), c_app(i, x)) -> 1 [1] app(i, c_app(c_app(., x), y)) -> app(app(., app(i, y)), app(i, x)) [1] app(c_app(., y), c_app(c_app(., c_app(i, y)), z)) -> z [1] encArg(.) -> . [0] encArg(1) -> 1 [0] encArg(i) -> i [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_. -> . [0] encode_1 -> 1 [0] encode_i -> i [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (19) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (20) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(i, 1) -> 1 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(i, c_app(i, x)) -> x [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(., c_app(i, x)), x) -> 1 [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(., 1), x) -> x [1] app(c_app(., x), 1) -> x [1] app(c_app(., c_app(c_app(., x), y)), z) -> app(app(., x), app(app(., y), z)) [1] app(c_app(., c_app(i, y)), c_app(c_app(., y), z)) -> z [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(., x), c_app(i, x)) -> 1 [1] app(i, c_app(c_app(., x), y)) -> app(app(., app(i, y)), app(i, x)) [1] app(c_app(., y), c_app(c_app(., c_app(i, y)), z)) -> z [1] encArg(.) -> . [0] encArg(1) -> 1 [0] encArg(i) -> i [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_. -> . [0] encode_1 -> 1 [0] encode_i -> i [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] The TRS has the following type information: app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app 1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app c_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app . :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encArg :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app cons_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_. :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app encode_false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app Rewrite Strategy: INNERMOST ---------------------------------------- (21) 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_. encode_1 encode_i encode_map encode_nil encode_cons encode_filter encode_filter2 encode_true encode_false app_2 Due to the following rules being added: encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_. -> null_encode_. [0] encode_1 -> null_encode_1 [0] encode_i -> null_encode_i [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_., null_encode_1, null_encode_i, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app ---------------------------------------- (22) 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(i, 1) -> 1 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(i, c_app(i, x)) -> x [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(., c_app(i, x)), x) -> 1 [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(., 1), x) -> x [1] app(c_app(., x), 1) -> x [1] app(c_app(., c_app(c_app(., x), y)), z) -> app(app(., x), app(app(., y), z)) [1] app(c_app(., c_app(i, y)), c_app(c_app(., y), z)) -> z [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(., x), c_app(i, x)) -> 1 [1] app(i, c_app(c_app(., x), y)) -> app(app(., app(i, y)), app(i, x)) [1] app(c_app(., y), c_app(c_app(., c_app(i, y)), z)) -> z [1] encArg(.) -> . [0] encArg(1) -> 1 [0] encArg(i) -> i [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_. -> . [0] encode_1 -> 1 [0] encode_i -> i [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_. -> null_encode_. [0] encode_1 -> null_encode_1 [0] encode_i -> null_encode_i [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app c_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app . :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encArg :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_. :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encArg :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_. :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (23) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (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(i, 1) -> 1 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(i, c_app(i, x)) -> x [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(c_app(filter, f), xs) [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(null_app, xs) [1] app(c_app(., c_app(i, x)), x) -> 1 [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(., 1), x) -> x [1] app(c_app(., x), 1) -> x [1] app(c_app(., c_app(c_app(., x), y)), z) -> app(c_app(., x), app(c_app(., y), z)) [1] app(c_app(., c_app(c_app(., x), y)), z) -> app(c_app(., x), app(null_app, z)) [1] app(c_app(., c_app(c_app(., x), y)), z) -> app(null_app, app(c_app(., y), z)) [1] app(c_app(., c_app(c_app(., x), y)), z) -> app(null_app, app(null_app, z)) [1] app(c_app(., c_app(i, y)), c_app(c_app(., y), z)) -> z [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(c_app(cons, x), app(c_app(filter, f), xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(c_app(cons, x), app(null_app, xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(null_app, app(c_app(filter, f), xs)) [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(null_app, app(null_app, xs)) [1] app(c_app(filter, i), c_app(c_app(cons, 1), xs)) -> app(app(app(app(filter2, 1), i), 1), xs) [2] app(c_app(filter, c_app(map, f5)), c_app(c_app(cons, c_app(c_app(cons, x9), xs1)), xs)) -> app(app(app(app(filter2, app(app(cons, app(f5, x9)), app(app(map, f5), xs1))), c_app(map, f5)), c_app(c_app(cons, x9), xs1)), xs) [2] app(c_app(filter, i), c_app(c_app(cons, c_app(i, x10)), xs)) -> app(app(app(app(filter2, x10), i), c_app(i, x10)), xs) [2] app(c_app(filter, c_app(c_app(c_app(filter2, false), f6), x11)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(filter, f6), x)), c_app(c_app(c_app(filter2, false), f6), x11)), x), xs) [2] app(c_app(filter, c_app(., c_app(i, x))), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, 1), c_app(., c_app(i, x))), x), xs) [2] app(c_app(filter, c_app(map, f7)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(map, f7)), nil), xs) [2] app(c_app(filter, c_app(filter, f8)), c_app(c_app(cons, nil), xs)) -> app(app(app(app(filter2, nil), c_app(filter, f8)), nil), xs) [2] app(c_app(filter, c_app(., 1)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, x), c_app(., 1)), x), xs) [2] app(c_app(filter, c_app(., x12)), c_app(c_app(cons, 1), xs)) -> app(app(app(app(filter2, x12), c_app(., x12)), 1), xs) [2] app(c_app(filter, c_app(., c_app(c_app(., x13), y3))), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(., x13), app(app(., y3), x))), c_app(., c_app(c_app(., x13), y3))), x), xs) [2] app(c_app(filter, c_app(., c_app(i, y4))), c_app(c_app(cons, c_app(c_app(., y4), z1)), xs)) -> app(app(app(app(filter2, z1), c_app(., c_app(i, y4))), c_app(c_app(., y4), z1)), xs) [2] app(c_app(filter, c_app(c_app(c_app(filter2, true), f9), x14)), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(app(cons, x14), app(app(filter, f9), x))), c_app(c_app(c_app(filter2, true), f9), x14)), x), xs) [2] app(c_app(filter, c_app(filter, f10)), c_app(c_app(cons, c_app(c_app(cons, x15), xs2)), xs)) -> app(app(app(app(filter2, app(app(app(app(filter2, app(f10, x15)), f10), x15), xs2)), c_app(filter, f10)), c_app(c_app(cons, x15), xs2)), xs) [2] app(c_app(filter, c_app(., x16)), c_app(c_app(cons, c_app(i, x16)), xs)) -> app(app(app(app(filter2, 1), c_app(., x16)), c_app(i, x16)), xs) [2] app(c_app(filter, i), c_app(c_app(cons, c_app(c_app(., x17), y5)), xs)) -> app(app(app(app(filter2, app(app(., app(i, y5)), app(i, x17))), i), c_app(c_app(., x17), y5)), xs) [2] app(c_app(filter, c_app(., y6)), c_app(c_app(cons, c_app(c_app(., c_app(i, y6)), z2)), xs)) -> app(app(app(app(filter2, z2), c_app(., y6)), c_app(c_app(., c_app(i, y6)), z2)), xs) [2] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, c_app(f, x)), f), x), xs) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, null_app), f), x), xs) [1] app(c_app(., x), c_app(i, x)) -> 1 [1] app(i, c_app(c_app(., x), y)) -> app(app(., app(i, y)), app(i, x)) [1] app(c_app(., y), c_app(c_app(., c_app(i, y)), z)) -> z [1] encArg(.) -> . [0] encArg(1) -> 1 [0] encArg(i) -> i [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_. -> . [0] encode_1 -> 1 [0] encode_i -> i [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_. -> null_encode_. [0] encode_1 -> null_encode_1 [0] encode_i -> null_encode_i [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app c_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app . :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encArg :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_. :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encArg :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_. :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (25) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: i => 6 1 => 1 map => 7 cons => 2 filter2 => 5 false => 3 filter => 4 . => 0 nil => 8 true => 9 null_encArg => 0 null_encode_app => 0 null_encode_. => 0 null_encode_1 => 0 null_encode_i => 0 null_encode_map => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_encode_filter2 => 0 null_encode_true => 0 null_encode_false => 0 null_app => 0 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: app(z', z'') -{ 1 }-> x :|: z'' = 1 + 6 + x, z' = 6, x >= 0 app(z', z'') -{ 1 }-> x :|: z' = 1 + 0 + 1, x >= 0, z'' = x app(z', z'') -{ 1 }-> x :|: x >= 0, z' = 1 + 0 + x, z'' = 1 app(z', z'') -{ 1 }-> z :|: z' = 1 + 0 + (1 + 6 + y), z >= 0, z'' = 1 + (1 + 0 + y) + z, y >= 0 app(z', z'') -{ 1 }-> z :|: z'' = 1 + (1 + 0 + (1 + 6 + y)) + z, z >= 0, y >= 0, z' = 1 + 0 + y app(z', z'') -{ 2 }-> app(app(app(app(5, x), 1 + 0 + 1), x), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, z' = 1 + 4 + (1 + 0 + 1) app(z', z'') -{ 2 }-> app(app(app(app(5, x10), 6), 1 + 6 + x10), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + (1 + 6 + x10)) + xs, z' = 1 + 4 + 6, x10 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, x12), 1 + 0 + x12), 1), xs) :|: z'' = 1 + (1 + 2 + 1) + xs, xs >= 0, x12 >= 0, z' = 1 + 4 + (1 + 0 + x12) app(z', z'') -{ 2 }-> app(app(app(app(5, z1), 1 + 0 + (1 + 6 + y4)), 1 + (1 + 0 + y4) + z1), xs) :|: xs >= 0, z1 >= 0, z' = 1 + 4 + (1 + 0 + (1 + 6 + y4)), z'' = 1 + (1 + 2 + (1 + (1 + 0 + y4) + z1)) + xs, y4 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, z2), 1 + 0 + y6), 1 + (1 + 0 + (1 + 6 + y6)) + z2), xs) :|: z' = 1 + 4 + (1 + 0 + y6), xs >= 0, y6 >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 0 + (1 + 6 + y6)) + z2)) + xs, z2 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(app(app(5, app(f10, x15)), f10), x15), xs2)), 1 + 4 + f10), 1 + (1 + 2 + x15) + xs2), xs) :|: xs >= 0, z' = 1 + 4 + (1 + 4 + f10), xs2 >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 2 + x15) + xs2)) + xs, f10 >= 0, x15 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(4, f6), x)), 1 + (1 + (1 + 5 + 3) + f6) + x11), x), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, z' = 1 + 4 + (1 + (1 + (1 + 5 + 3) + f6) + x11), f6 >= 0, x11 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(2, x14), app(app(4, f9), x))), 1 + (1 + (1 + 5 + 9) + f9) + x14), x), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, z' = 1 + 4 + (1 + (1 + (1 + 5 + 9) + f9) + x14), x14 >= 0, f9 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(2, app(f5, x9)), app(app(7, f5), xs1))), 1 + 7 + f5), 1 + (1 + 2 + x9) + xs1), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 2 + x9) + xs1)) + xs, xs1 >= 0, z' = 1 + 4 + (1 + 7 + f5), f5 >= 0, x9 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(0, x13), app(app(0, y3), x))), 1 + 0 + (1 + (1 + 0 + x13) + y3)), x), xs) :|: x13 >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, y3 >= 0, z' = 1 + 4 + (1 + 0 + (1 + (1 + 0 + x13) + y3)) app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(0, app(6, y5)), app(6, x17))), 6), 1 + (1 + 0 + x17) + y5), xs) :|: y5 >= 0, xs >= 0, x17 >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 0 + x17) + y5)) + xs, z' = 1 + 4 + 6 app(z', z'') -{ 2 }-> app(app(app(app(5, 8), 1 + 7 + f7), 8), xs) :|: xs >= 0, f7 >= 0, z' = 1 + 4 + (1 + 7 + f7), z'' = 1 + (1 + 2 + 8) + xs app(z', z'') -{ 2 }-> app(app(app(app(5, 8), 1 + 4 + f8), 8), xs) :|: f8 >= 0, xs >= 0, z' = 1 + 4 + (1 + 4 + f8), z'' = 1 + (1 + 2 + 8) + xs app(z', z'') -{ 2 }-> app(app(app(app(5, 1), 6), 1), xs) :|: z'' = 1 + (1 + 2 + 1) + xs, xs >= 0, z' = 1 + 4 + 6 app(z', z'') -{ 2 }-> app(app(app(app(5, 1), 1 + 0 + x16), 1 + 6 + x16), xs) :|: xs >= 0, z' = 1 + 4 + (1 + 0 + x16), z'' = 1 + (1 + 2 + (1 + 6 + x16)) + xs, x16 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, 1), 1 + 0 + (1 + 6 + x)), x), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + x) + xs, z' = 1 + 4 + (1 + 0 + (1 + 6 + x)), x >= 0 app(z', z'') -{ 1 }-> app(app(app(app(5, 0), f), x), xs) :|: f >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, z' = 1 + 4 + f, x >= 0 app(z', z'') -{ 1 }-> app(app(app(app(5, 1 + f + x), f), x), xs) :|: f >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, z' = 1 + 4 + f, x >= 0 app(z', z'') -{ 1 }-> app(app(2, app(f, x)), app(app(7, f), xs)) :|: f >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, z' = 1 + 7 + f app(z', z'') -{ 1 }-> app(app(0, app(6, y)), app(6, x)) :|: z' = 6, x >= 0, y >= 0, z'' = 1 + (1 + 0 + x) + y app(z', z'') -{ 1 }-> app(0, xs) :|: f >= 0, z' = 1 + (1 + (1 + 5 + 3) + f) + x, xs >= 0, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(0, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(0, app(0, z)) :|: z'' = z, z >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> app(0, app(1 + 4 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(0, app(1 + 0 + y, z)) :|: z'' = z, z >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> app(1 + 4 + f, xs) :|: f >= 0, z' = 1 + (1 + (1 + 5 + 3) + f) + x, xs >= 0, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(1 + 2 + x, app(0, xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(1 + 2 + x, app(1 + 4 + f, xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(1 + 0 + x, app(0, z)) :|: z'' = z, z >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> app(1 + 0 + x, app(1 + 0 + y, z)) :|: z'' = z, z >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> 8 :|: f >= 0, z'' = 8, z' = 1 + 7 + f app(z', z'') -{ 1 }-> 8 :|: f >= 0, z' = 1 + 4 + f, z'' = 8 app(z', z'') -{ 1 }-> 1 :|: z' = 6, z'' = 1 app(z', z'') -{ 1 }-> 1 :|: z' = 1 + 0 + (1 + 6 + x), x >= 0, z'' = x app(z', z'') -{ 1 }-> 1 :|: z'' = 1 + 6 + x, x >= 0, z' = 1 + 0 + x app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 app(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0 encArg(z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2 encArg(z') -{ 0 }-> 9 :|: z' = 9 encArg(z') -{ 0 }-> 8 :|: z' = 8 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_. -{ 0 }-> 0 :|: encode_1 -{ 0 }-> 1 :|: encode_1 -{ 0 }-> 0 :|: encode_app(z', z'') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2 encode_app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 encode_cons -{ 0 }-> 2 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_i -{ 0 }-> 6 :|: encode_i -{ 0 }-> 0 :|: encode_map -{ 0 }-> 7 :|: encode_map -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 8 :|: encode_nil -{ 0 }-> 0 :|: encode_true -{ 0 }-> 9 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (27) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (28) Obligation: Complexity RNTS consisting of the following rules: app(z', z'') -{ 1 }-> z :|: z >= 0, z'' = 1 + (1 + 0 + (z' - 8)) + z, z' - 8 >= 0 app(z', z'') -{ 1 }-> z :|: z'' = 1 + (1 + 0 + (1 + 6 + (z' - 1))) + z, z >= 0, z' - 1 >= 0 app(z', z'') -{ 1 }-> z'' :|: z' = 1 + 0 + 1, z'' >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, x), 1 + 0 + 1), x), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, z' = 1 + 4 + (1 + 0 + 1) app(z', z'') -{ 2 }-> app(app(app(app(5, x10), 6), 1 + 6 + x10), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + (1 + 6 + x10)) + xs, z' = 1 + 4 + 6, x10 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, z1), 1 + 0 + (1 + 6 + (z' - 13))), 1 + (1 + 0 + (z' - 13)) + z1), xs) :|: xs >= 0, z1 >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 0 + (z' - 13)) + z1)) + xs, z' - 13 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, z2), 1 + 0 + (z' - 6)), 1 + (1 + 0 + (1 + 6 + (z' - 6))) + z2), xs) :|: xs >= 0, z' - 6 >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 0 + (1 + 6 + (z' - 6))) + z2)) + xs, z2 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(app(app(5, app(z' - 10, x15)), z' - 10), x15), xs2)), 1 + 4 + (z' - 10)), 1 + (1 + 2 + x15) + xs2), xs) :|: xs >= 0, xs2 >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 2 + x15) + xs2)) + xs, z' - 10 >= 0, x15 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(4, f6), x)), 1 + (1 + (1 + 5 + 3) + f6) + x11), x), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, z' = 1 + 4 + (1 + (1 + (1 + 5 + 3) + f6) + x11), f6 >= 0, x11 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(2, x14), app(app(4, f9), x))), 1 + (1 + (1 + 5 + 9) + f9) + x14), x), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, z' = 1 + 4 + (1 + (1 + (1 + 5 + 9) + f9) + x14), x14 >= 0, f9 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(2, app(z' - 13, x9)), app(app(7, z' - 13), xs1))), 1 + 7 + (z' - 13)), 1 + (1 + 2 + x9) + xs1), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 2 + x9) + xs1)) + xs, xs1 >= 0, z' - 13 >= 0, x9 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(0, x13), app(app(0, y3), x))), 1 + 0 + (1 + (1 + 0 + x13) + y3)), x), xs) :|: x13 >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, y3 >= 0, z' = 1 + 4 + (1 + 0 + (1 + (1 + 0 + x13) + y3)) app(z', z'') -{ 2 }-> app(app(app(app(5, app(app(0, app(6, y5)), app(6, x17))), 6), 1 + (1 + 0 + x17) + y5), xs) :|: y5 >= 0, xs >= 0, x17 >= 0, z'' = 1 + (1 + 2 + (1 + (1 + 0 + x17) + y5)) + xs, z' = 1 + 4 + 6 app(z', z'') -{ 2 }-> app(app(app(app(5, 8), 1 + 7 + (z' - 13)), 8), z'' - 12) :|: z'' - 12 >= 0, z' - 13 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, 8), 1 + 4 + (z' - 10)), 8), z'' - 12) :|: z' - 10 >= 0, z'' - 12 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, 1), 6), 1), z'' - 5) :|: z'' - 5 >= 0, z' = 1 + 4 + 6 app(z', z'') -{ 2 }-> app(app(app(app(5, 1), 1 + 0 + (z' - 6)), 1 + 6 + (z' - 6)), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + (1 + 6 + (z' - 6))) + xs, z' - 6 >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, 1), 1 + 0 + (1 + 6 + (z' - 13))), z' - 13), xs) :|: xs >= 0, z'' = 1 + (1 + 2 + (z' - 13)) + xs, z' - 13 >= 0 app(z', z'') -{ 1 }-> app(app(app(app(5, 0), z' - 5), x), xs) :|: z' - 5 >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0 app(z', z'') -{ 2 }-> app(app(app(app(5, z' - 6), 1 + 0 + (z' - 6)), 1), z'' - 5) :|: z'' - 5 >= 0, z' - 6 >= 0 app(z', z'') -{ 1 }-> app(app(app(app(5, 1 + (z' - 5) + x), z' - 5), x), xs) :|: z' - 5 >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0 app(z', z'') -{ 1 }-> app(app(2, app(z' - 8, x)), app(app(7, z' - 8), xs)) :|: z' - 8 >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0 app(z', z'') -{ 1 }-> app(app(0, app(6, y)), app(6, x)) :|: z' = 6, x >= 0, y >= 0, z'' = 1 + (1 + 0 + x) + y app(z', z'') -{ 1 }-> app(0, z'') :|: f >= 0, z' = 1 + (1 + (1 + 5 + 3) + f) + x, z'' >= 0, x >= 0 app(z', z'') -{ 1 }-> app(0, app(0, z'')) :|: z'' >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> app(0, app(0, z'')) :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(0, app(1 + 4 + f, z'')) :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(0, app(1 + 0 + y, z'')) :|: z'' >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> app(1 + 4 + f, z'') :|: f >= 0, z' = 1 + (1 + (1 + 5 + 3) + f) + x, z'' >= 0, x >= 0 app(z', z'') -{ 1 }-> app(1 + 2 + x, app(0, z'')) :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(1 + 2 + x, app(1 + 4 + f, z'')) :|: f >= 0, z'' >= 0, x >= 0, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(1 + 0 + x, app(0, z'')) :|: z'' >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> app(1 + 0 + x, app(1 + 0 + y, z'')) :|: z'' >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> 8 :|: z' - 8 >= 0, z'' = 8 app(z', z'') -{ 1 }-> 8 :|: z' - 5 >= 0, z'' = 8 app(z', z'') -{ 1 }-> 1 :|: z' = 6, z'' = 1 app(z', z'') -{ 1 }-> 1 :|: z' - 8 >= 0, z'' = z' - 8 app(z', z'') -{ 1 }-> 1 :|: z'' - 7 >= 0, z' = 1 + 0 + (z'' - 7) app(z', z'') -{ 0 }-> 0 :|: z' >= 0, z'' >= 0 app(z', z'') -{ 1 }-> z' - 1 :|: z' - 1 >= 0, z'' = 1 app(z', z'') -{ 1 }-> z'' - 7 :|: z' = 6, z'' - 7 >= 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, x_2 >= 0, z' = 1 + x_1 + x_2 encArg(z') -{ 0 }-> 9 :|: z' = 9 encArg(z') -{ 0 }-> 8 :|: z' = 8 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_. -{ 0 }-> 0 :|: encode_1 -{ 0 }-> 1 :|: encode_1 -{ 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 }-> 2 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_i -{ 0 }-> 6 :|: encode_i -{ 0 }-> 0 :|: encode_map -{ 0 }-> 7 :|: encode_map -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 8 :|: encode_nil -{ 0 }-> 0 :|: encode_true -{ 0 }-> 9 :|: encode_true -{ 0 }-> 0 :|: ---------------------------------------- (29) 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_. -> null_encode_. [0] encode_1 -> null_encode_1 [0] encode_i -> null_encode_i [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] And the following fresh constants: null_encArg, null_encode_app, null_encode_., null_encode_1, null_encode_i, null_encode_map, null_encode_nil, null_encode_cons, null_encode_filter, null_encode_filter2, null_encode_true, null_encode_false, null_app ---------------------------------------- (30) 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(i, 1) -> 1 [1] app(c_app(map, f), c_app(c_app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) [1] app(i, c_app(i, x)) -> x [1] app(c_app(c_app(c_app(filter2, false), f), x), xs) -> app(app(filter, f), xs) [1] app(c_app(., c_app(i, x)), x) -> 1 [1] app(c_app(map, f), nil) -> nil [1] app(c_app(filter, f), nil) -> nil [1] app(c_app(., 1), x) -> x [1] app(c_app(., x), 1) -> x [1] app(c_app(., c_app(c_app(., x), y)), z) -> app(app(., x), app(app(., y), z)) [1] app(c_app(., c_app(i, y)), c_app(c_app(., y), z)) -> z [1] app(c_app(c_app(c_app(filter2, true), f), x), xs) -> app(app(cons, x), app(app(filter, f), xs)) [1] app(c_app(filter, f), c_app(c_app(cons, x), xs)) -> app(app(app(app(filter2, app(f, x)), f), x), xs) [1] app(c_app(., x), c_app(i, x)) -> 1 [1] app(i, c_app(c_app(., x), y)) -> app(app(., app(i, y)), app(i, x)) [1] app(c_app(., y), c_app(c_app(., c_app(i, y)), z)) -> z [1] encArg(.) -> . [0] encArg(1) -> 1 [0] encArg(i) -> i [0] encArg(map) -> map [0] encArg(nil) -> nil [0] encArg(cons) -> cons [0] encArg(filter) -> filter [0] encArg(filter2) -> filter2 [0] encArg(true) -> true [0] encArg(false) -> false [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_. -> . [0] encode_1 -> 1 [0] encode_i -> i [0] encode_map -> map [0] encode_nil -> nil [0] encode_cons -> cons [0] encode_filter -> filter [0] encode_filter2 -> filter2 [0] encode_true -> true [0] encode_false -> false [0] app(x0, x1) -> c_app(x0, x1) [0] encArg(v0) -> null_encArg [0] encode_app(v0, v1) -> null_encode_app [0] encode_. -> null_encode_. [0] encode_1 -> null_encode_1 [0] encode_i -> null_encode_i [0] encode_map -> null_encode_map [0] encode_nil -> null_encode_nil [0] encode_cons -> null_encode_cons [0] encode_filter -> null_encode_filter [0] encode_filter2 -> null_encode_filter2 [0] encode_true -> null_encode_true [0] encode_false -> null_encode_false [0] app(v0, v1) -> null_app [0] The TRS has the following type information: app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app 1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app c_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app . :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encArg :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app cons_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app -> i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_. :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app encode_false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encArg :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_. :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_1 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_i :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_map :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_nil :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_cons :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_filter2 :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_true :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_encode_false :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app null_app :: i:1:map:c_app:cons:filter2:false:filter:.:nil:true:cons_app:null_encArg:null_encode_app:null_encode_.:null_encode_1:null_encode_i:null_encode_map:null_encode_nil:null_encode_cons:null_encode_filter:null_encode_filter2:null_encode_true:null_encode_false:null_app Rewrite Strategy: INNERMOST ---------------------------------------- (31) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: i => 6 1 => 1 map => 7 cons => 2 filter2 => 5 false => 3 filter => 4 . => 0 nil => 8 true => 9 null_encArg => 0 null_encode_app => 0 null_encode_. => 0 null_encode_1 => 0 null_encode_i => 0 null_encode_map => 0 null_encode_nil => 0 null_encode_cons => 0 null_encode_filter => 0 null_encode_filter2 => 0 null_encode_true => 0 null_encode_false => 0 null_app => 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: app(z', z'') -{ 1 }-> x :|: z'' = 1 + 6 + x, z' = 6, x >= 0 app(z', z'') -{ 1 }-> x :|: z' = 1 + 0 + 1, x >= 0, z'' = x app(z', z'') -{ 1 }-> x :|: x >= 0, z' = 1 + 0 + x, z'' = 1 app(z', z'') -{ 1 }-> z :|: z' = 1 + 0 + (1 + 6 + y), z >= 0, z'' = 1 + (1 + 0 + y) + z, y >= 0 app(z', z'') -{ 1 }-> z :|: z'' = 1 + (1 + 0 + (1 + 6 + y)) + z, z >= 0, y >= 0, z' = 1 + 0 + y app(z', z'') -{ 1 }-> app(app(app(app(5, app(f, x)), f), x), xs) :|: f >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, z' = 1 + 4 + f, x >= 0 app(z', z'') -{ 1 }-> app(app(4, f), xs) :|: f >= 0, z' = 1 + (1 + (1 + 5 + 3) + f) + x, xs >= 0, x >= 0, z'' = xs app(z', z'') -{ 1 }-> app(app(2, x), app(app(4, f), xs)) :|: f >= 0, xs >= 0, x >= 0, z'' = xs, z' = 1 + (1 + (1 + 5 + 9) + f) + x app(z', z'') -{ 1 }-> app(app(2, app(f, x)), app(app(7, f), xs)) :|: f >= 0, xs >= 0, z'' = 1 + (1 + 2 + x) + xs, x >= 0, z' = 1 + 7 + f app(z', z'') -{ 1 }-> app(app(0, x), app(app(0, y), z)) :|: z'' = z, z >= 0, x >= 0, y >= 0, z' = 1 + 0 + (1 + (1 + 0 + x) + y) app(z', z'') -{ 1 }-> app(app(0, app(6, y)), app(6, x)) :|: z' = 6, x >= 0, y >= 0, z'' = 1 + (1 + 0 + x) + y app(z', z'') -{ 1 }-> 8 :|: f >= 0, z'' = 8, z' = 1 + 7 + f app(z', z'') -{ 1 }-> 8 :|: f >= 0, z' = 1 + 4 + f, z'' = 8 app(z', z'') -{ 1 }-> 1 :|: z' = 6, z'' = 1 app(z', z'') -{ 1 }-> 1 :|: z' = 1 + 0 + (1 + 6 + x), x >= 0, z'' = x app(z', z'') -{ 1 }-> 1 :|: z'' = 1 + 6 + x, x >= 0, z' = 1 + 0 + x app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 app(z', z'') -{ 0 }-> 1 + x0 + x1 :|: z'' = x1, x0 >= 0, x1 >= 0, z' = x0 encArg(z') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, x_2 >= 0, z' = 1 + x_1 + x_2 encArg(z') -{ 0 }-> 9 :|: z' = 9 encArg(z') -{ 0 }-> 8 :|: z' = 8 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_. -{ 0 }-> 0 :|: encode_1 -{ 0 }-> 1 :|: encode_1 -{ 0 }-> 0 :|: encode_app(z', z'') -{ 0 }-> app(encArg(x_1), encArg(x_2)) :|: x_1 >= 0, z' = x_1, x_2 >= 0, z'' = x_2 encode_app(z', z'') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z'' = v1, z' = v0 encode_cons -{ 0 }-> 2 :|: encode_cons -{ 0 }-> 0 :|: encode_false -{ 0 }-> 3 :|: encode_false -{ 0 }-> 0 :|: encode_filter -{ 0 }-> 4 :|: encode_filter -{ 0 }-> 0 :|: encode_filter2 -{ 0 }-> 5 :|: encode_filter2 -{ 0 }-> 0 :|: encode_i -{ 0 }-> 6 :|: encode_i -{ 0 }-> 0 :|: encode_map -{ 0 }-> 7 :|: encode_map -{ 0 }-> 0 :|: encode_nil -{ 0 }-> 8 :|: encode_nil -{ 0 }-> 0 :|: encode_true -{ 0 }-> 9 :|: encode_true -{ 0 }-> 0 :|: Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (33) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (34) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(.) -> c ENCARG(1) -> c1 ENCARG(i) -> c2 ENCARG(map) -> c3 ENCARG(nil) -> c4 ENCARG(cons) -> c5 ENCARG(filter) -> c6 ENCARG(filter2) -> c7 ENCARG(true) -> c8 ENCARG(false) -> c9 ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_. -> c12 ENCODE_1 -> c13 ENCODE_I -> c14 ENCODE_MAP -> c15 ENCODE_NIL -> c16 ENCODE_CONS -> c17 ENCODE_FILTER -> c18 ENCODE_FILTER2 -> c19 ENCODE_TRUE -> c20 ENCODE_FALSE -> c21 APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(., z0), APP(app(., z1), z2), APP(., z1)) APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(., app(i, z1)), APP(i, z1), APP(i, z0)) APP(app(map, z0), nil) -> c32 APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c34 APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(., z0), APP(app(., z1), z2), APP(., z1)) APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(., app(i, z1)), APP(i, z1), APP(i, z0)) APP(app(map, z0), nil) -> c32 APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c34 APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_., encode_1, encode_i, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, ENCODE_., ENCODE_1, ENCODE_I, ENCODE_MAP, ENCODE_NIL, ENCODE_CONS, ENCODE_FILTER, ENCODE_FILTER2, ENCODE_TRUE, ENCODE_FALSE, APP_2 Compound Symbols: c, c1, c2, c3, c4, c5, c6, c7, c8, c9, c10_3, c11_3, c12, c13, c14, c15, c16, c17, c18, c19, c20, c21, c22, c23, c24, c25, c26, c27, c28_4, c29, c30, c31_4, c32, c33_5, c34, c35_5, c36_4, c37_2 ---------------------------------------- (35) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 20 trailing nodes: ENCODE_NIL -> c16 ENCARG(nil) -> c4 ENCODE_CONS -> c17 ENCODE_FILTER2 -> c19 ENCODE_I -> c14 ENCARG(filter) -> c6 ENCARG(1) -> c1 ENCARG(cons) -> c5 ENCARG(false) -> c9 ENCODE_MAP -> c15 ENCARG(i) -> c2 ENCODE_1 -> c13 ENCODE_FILTER -> c18 ENCARG(filter2) -> c7 ENCARG(map) -> c3 ENCODE_TRUE -> c20 ENCARG(true) -> c8 ENCODE_. -> c12 ENCARG(.) -> c ENCODE_FALSE -> c21 ---------------------------------------- (36) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(., z0), APP(app(., z1), z2), APP(., z1)) APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(., app(i, z1)), APP(i, z1), APP(i, z0)) APP(app(map, z0), nil) -> c32 APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c34 APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2), APP(filter, z0)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(., z0), APP(app(., z1), z2), APP(., z1)) APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(., app(i, z1)), APP(i, z1), APP(i, z0)) APP(app(map, z0), nil) -> c32 APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(app(cons, app(z0, z1)), app(app(map, z0), z2)), APP(cons, app(z0, z1)), APP(z0, z1), APP(app(map, z0), z2), APP(map, z0)) APP(app(filter, z0), nil) -> c34 APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(app(app(filter2, app(z0, z1)), z0), z1), APP(app(filter2, app(z0, z1)), z0), APP(filter2, app(z0, z1)), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(cons, z1), app(app(filter, z0), z2)), APP(cons, z1), APP(app(filter, z0), z2), APP(filter, z0)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2), APP(filter, z0)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_., encode_1, encode_i, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c10_3, c11_3, c22, c23, c24, c25, c26, c27, c28_4, c29, c30, c31_4, c32, c33_5, c34, c35_5, c36_4, c37_2 ---------------------------------------- (37) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 13 trailing tuple parts ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) ENCODE_APP(z0, z1) -> c11(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_., encode_1, encode_i, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, ENCODE_APP_2, APP_2 Compound Symbols: c10_3, c11_3, c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c31_3, c33_2, c35_2, c36_1, c37_1 ---------------------------------------- (39) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, 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(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_., encode_1, encode_i, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c10_3, c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c31_3, c33_2, c35_2, c36_1, c37_1, c_1 ---------------------------------------- (41) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 2 leading nodes: ENCODE_APP(z0, z1) -> c(ENCARG(z0)) ENCODE_APP(z0, z1) -> c(ENCARG(z1)) ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: app_2, encArg_1, encode_app_2, encode_., encode_1, encode_i, encode_map, encode_nil, encode_cons, encode_filter, encode_filter2, encode_true, encode_false Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c10_3, c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c31_3, c33_2, c35_2, c36_1, c37_1, c_1 ---------------------------------------- (43) CdtUsableRulesProof (BOTH BOUNDS(ID, ID)) The following rules are not usable and were removed: encode_app(z0, z1) -> app(encArg(z0), encArg(z1)) encode_. -> . encode_1 -> 1 encode_i -> i encode_map -> map encode_nil -> nil encode_cons -> cons encode_filter -> filter encode_filter2 -> filter2 encode_true -> true encode_false -> false ---------------------------------------- (44) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: ENCARG_1, APP_2, ENCODE_APP_2 Compound Symbols: c10_3, c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c31_3, c33_2, c35_2, c36_1, c37_1, c_1 ---------------------------------------- (45) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(z0, z1)) -> c10(APP(encArg(z0), encArg(z1)), ENCARG(z0), ENCARG(z1)) by ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0), ENCARG(.)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0), ENCARG(1)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0), ENCARG(i)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(., x1)) -> c10(APP(., encArg(x1)), ENCARG(.), ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(APP(1, encArg(x1)), ENCARG(1), ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(i), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ---------------------------------------- (46) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0), ENCARG(.)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0), ENCARG(1)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0), ENCARG(i)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0), ENCARG(map)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0), ENCARG(nil)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0), ENCARG(cons)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0), ENCARG(filter)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0), ENCARG(filter2)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0), ENCARG(true)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0), ENCARG(false)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(., x1)) -> c10(APP(., encArg(x1)), ENCARG(.), ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(APP(1, encArg(x1)), ENCARG(1), ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(i), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(APP(map, encArg(x1)), ENCARG(map), ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(APP(nil, encArg(x1)), ENCARG(nil), ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(APP(cons, encArg(x1)), ENCARG(cons), ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(APP(filter, encArg(x1)), ENCARG(filter), ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(APP(filter2, encArg(x1)), ENCARG(filter2), ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(APP(true, encArg(x1)), ENCARG(true), ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(APP(false, encArg(x1)), ENCARG(false), ENCARG(x1)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c31_3, c33_2, c35_2, c36_1, c37_1, c_1, c10_3 ---------------------------------------- (47) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 29 trailing tuple parts ---------------------------------------- (48) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c31_3, c33_2, c35_2, c36_1, c37_1, c_1, c10_3, c10_2, c10_1 ---------------------------------------- (49) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(i, app(app(., z0), z1)) -> c31(APP(app(., app(i, z1)), app(i, z0)), APP(i, z1), APP(i, z0)) by APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) ---------------------------------------- (50) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c35_2, c36_1, c37_1, c_1, c10_3, c10_2, c10_1, c31_3, c31_2 ---------------------------------------- (51) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, z0), app(app(cons, z1), z2)) -> c35(APP(app(app(app(filter2, app(z0, z1)), z0), z1), z2), APP(z0, z1)) by APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, 1), app(., app(i, z0))), z0), x2), APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, 1), app(., z0)), app(i, z0)), x2), APP(app(., z0), app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, 1), i), 1), x2), APP(i, 1)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) ---------------------------------------- (52) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, 1), app(., app(i, z0))), z0), x2), APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, 1), app(., z0)), app(i, z0)), x2), APP(app(., z0), app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, 1), i), 1), x2), APP(i, 1)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, 1), app(., app(i, z0))), z0), x2), APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, 1), app(., z0)), app(i, z0)), x2), APP(app(., z0), app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, 1), i), 1), x2), APP(i, 1)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(app(app(filter2, nil), app(map, z0)), nil), x2), APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2), APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(app(app(filter2, nil), app(filter, z0)), nil), x2), APP(app(filter, z0), nil)) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2), APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c_1, c10_3, c10_2, c10_1, c31_3, c31_2, c35_2 ---------------------------------------- (53) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (54) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCODE_APP_2, ENCARG_1 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c_1, c10_3, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1 ---------------------------------------- (55) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(z0, z1) -> c(APP(encArg(z0), encArg(z1))) by ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(., x1) -> c(APP(., encArg(x1))) ENCODE_APP(1, x1) -> c(APP(1, encArg(x1))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, 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(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(., x1) -> c(APP(., encArg(x1))) ENCODE_APP(1, x1) -> c(APP(1, encArg(x1))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_3, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1 ---------------------------------------- (57) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 9 trailing nodes: ENCODE_APP(cons, x1) -> c(APP(cons, encArg(x1))) ENCODE_APP(filter, x1) -> c(APP(filter, encArg(x1))) ENCODE_APP(., x1) -> c(APP(., encArg(x1))) ENCODE_APP(map, x1) -> c(APP(map, encArg(x1))) ENCODE_APP(1, x1) -> c(APP(1, encArg(x1))) ENCODE_APP(false, x1) -> c(APP(false, encArg(x1))) ENCODE_APP(true, x1) -> c(APP(true, encArg(x1))) ENCODE_APP(nil, x1) -> c(APP(nil, encArg(x1))) ENCODE_APP(filter2, x1) -> c(APP(filter2, encArg(x1))) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_3, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1 ---------------------------------------- (59) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons_app(z0, z1))) -> c10(APP(encArg(x0), app(encArg(z0), encArg(z1))), ENCARG(x0), ENCARG(cons_app(z0, z1))) by ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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(x1, x2))) -> c10(APP(., app(encArg(x1), encArg(x2))), ENCARG(.), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(APP(1, app(encArg(x1), encArg(x2))), ENCARG(1), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(i), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c10(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(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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(x1, x2))) -> c10(APP(., app(encArg(x1), encArg(x2))), ENCARG(.), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(APP(1, app(encArg(x1), encArg(x2))), ENCARG(1), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(i), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(APP(map, app(encArg(x1), encArg(x2))), ENCARG(map), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(APP(nil, app(encArg(x1), encArg(x2))), ENCARG(nil), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(APP(cons, app(encArg(x1), encArg(x2))), ENCARG(cons), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(APP(filter, app(encArg(x1), encArg(x2))), ENCARG(filter), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(APP(filter2, app(encArg(x1), encArg(x2))), ENCARG(filter2), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(APP(true, app(encArg(x1), encArg(x2))), ENCARG(true), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(APP(false, app(encArg(x1), encArg(x2))), ENCARG(false), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(z0, z1), cons_app(x1, x2))) -> c10(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(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_3, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1 ---------------------------------------- (61) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 19 trailing tuple parts ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_3, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1 ---------------------------------------- (63) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(cons_app(z0, z1), x1)) -> c10(APP(app(encArg(z0), encArg(z1)), encArg(x1)), ENCARG(cons_app(z0, z1)), ENCARG(x1)) by ENCARG(cons_app(cons_app(x0, x1), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)), ENCARG(.)) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1)), ENCARG(1)) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1)), ENCARG(i)) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, x1), cons_app(z0, z1))) -> c10(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, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(APP(app(1, encArg(x1)), encArg(x2)), ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, x1), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1)), ENCARG(.)) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1)), ENCARG(1)) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1)), ENCARG(i)) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1)), ENCARG(map)) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1)), ENCARG(nil)) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1)), ENCARG(cons)) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1)), ENCARG(filter)) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1)), ENCARG(filter2)) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1)), ENCARG(true)) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1)), ENCARG(false)) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(APP(app(1, encArg(x1)), encArg(x2)), ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(APP(app(nil, encArg(x1)), encArg(x2)), ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(APP(app(cons, encArg(x1)), encArg(x2)), ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(APP(app(filter2, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(APP(app(true, encArg(x1)), encArg(x2)), ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(APP(app(false, encArg(x1)), encArg(x2)), ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (65) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 16 trailing tuple parts ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (67) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, .)) -> c10(APP(encArg(x0), .), ENCARG(x0)) by ENCARG(cons_app(., .)) -> c10(APP(., .), ENCARG(.)) ENCARG(cons_app(1, .)) -> c10(APP(1, .), ENCARG(1)) ENCARG(cons_app(i, .)) -> c10(APP(i, .), ENCARG(i)) ENCARG(cons_app(map, .)) -> c10(APP(map, .), ENCARG(map)) ENCARG(cons_app(nil, .)) -> c10(APP(nil, .), ENCARG(nil)) ENCARG(cons_app(cons, .)) -> c10(APP(cons, .), ENCARG(cons)) ENCARG(cons_app(filter, .)) -> c10(APP(filter, .), ENCARG(filter)) ENCARG(cons_app(filter2, .)) -> c10(APP(filter2, .), ENCARG(filter2)) ENCARG(cons_app(true, .)) -> c10(APP(true, .), ENCARG(true)) ENCARG(cons_app(false, .)) -> c10(APP(false, .), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), .)) -> c10(APP(app(encArg(z0), encArg(z1)), .), ENCARG(cons_app(z0, z1))) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(., .)) -> c10(APP(., .), ENCARG(.)) ENCARG(cons_app(1, .)) -> c10(APP(1, .), ENCARG(1)) ENCARG(cons_app(i, .)) -> c10(APP(i, .), ENCARG(i)) ENCARG(cons_app(map, .)) -> c10(APP(map, .), ENCARG(map)) ENCARG(cons_app(nil, .)) -> c10(APP(nil, .), ENCARG(nil)) ENCARG(cons_app(cons, .)) -> c10(APP(cons, .), ENCARG(cons)) ENCARG(cons_app(filter, .)) -> c10(APP(filter, .), ENCARG(filter)) ENCARG(cons_app(filter2, .)) -> c10(APP(filter2, .), ENCARG(filter2)) ENCARG(cons_app(true, .)) -> c10(APP(true, .), ENCARG(true)) ENCARG(cons_app(false, .)) -> c10(APP(false, .), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (69) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(i, .)) -> c10(APP(i, .), ENCARG(i)) ENCARG(cons_app(nil, .)) -> c10(APP(nil, .), ENCARG(nil)) ENCARG(cons_app(filter, .)) -> c10(APP(filter, .), ENCARG(filter)) ENCARG(cons_app(true, .)) -> c10(APP(true, .), ENCARG(true)) ENCARG(cons_app(cons, .)) -> c10(APP(cons, .), ENCARG(cons)) ENCARG(cons_app(false, .)) -> c10(APP(false, .), ENCARG(false)) ENCARG(cons_app(1, .)) -> c10(APP(1, .), ENCARG(1)) ENCARG(cons_app(., .)) -> c10(APP(., .), ENCARG(.)) ENCARG(cons_app(filter2, .)) -> c10(APP(filter2, .), ENCARG(filter2)) ENCARG(cons_app(map, .)) -> c10(APP(map, .), ENCARG(map)) ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, 1)) -> c10(APP(encArg(x0), 1), ENCARG(x0)) by ENCARG(cons_app(., 1)) -> c10(APP(., 1), ENCARG(.)) ENCARG(cons_app(1, 1)) -> c10(APP(1, 1), ENCARG(1)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1), ENCARG(i)) ENCARG(cons_app(map, 1)) -> c10(APP(map, 1), ENCARG(map)) ENCARG(cons_app(nil, 1)) -> c10(APP(nil, 1), ENCARG(nil)) ENCARG(cons_app(cons, 1)) -> c10(APP(cons, 1), ENCARG(cons)) ENCARG(cons_app(filter, 1)) -> c10(APP(filter, 1), ENCARG(filter)) ENCARG(cons_app(filter2, 1)) -> c10(APP(filter2, 1), ENCARG(filter2)) ENCARG(cons_app(true, 1)) -> c10(APP(true, 1), ENCARG(true)) ENCARG(cons_app(false, 1)) -> c10(APP(false, 1), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), 1)) -> c10(APP(app(encArg(z0), encArg(z1)), 1), ENCARG(cons_app(z0, z1))) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(., 1)) -> c10(APP(., 1), ENCARG(.)) ENCARG(cons_app(1, 1)) -> c10(APP(1, 1), ENCARG(1)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1), ENCARG(i)) ENCARG(cons_app(map, 1)) -> c10(APP(map, 1), ENCARG(map)) ENCARG(cons_app(nil, 1)) -> c10(APP(nil, 1), ENCARG(nil)) ENCARG(cons_app(cons, 1)) -> c10(APP(cons, 1), ENCARG(cons)) ENCARG(cons_app(filter, 1)) -> c10(APP(filter, 1), ENCARG(filter)) ENCARG(cons_app(filter2, 1)) -> c10(APP(filter2, 1), ENCARG(filter2)) ENCARG(cons_app(true, 1)) -> c10(APP(true, 1), ENCARG(true)) ENCARG(cons_app(false, 1)) -> c10(APP(false, 1), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (73) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 9 trailing nodes: ENCARG(cons_app(true, 1)) -> c10(APP(true, 1), ENCARG(true)) ENCARG(cons_app(filter2, 1)) -> c10(APP(filter2, 1), ENCARG(filter2)) ENCARG(cons_app(map, 1)) -> c10(APP(map, 1), ENCARG(map)) ENCARG(cons_app(false, 1)) -> c10(APP(false, 1), ENCARG(false)) ENCARG(cons_app(filter, 1)) -> c10(APP(filter, 1), ENCARG(filter)) ENCARG(cons_app(nil, 1)) -> c10(APP(nil, 1), ENCARG(nil)) ENCARG(cons_app(cons, 1)) -> c10(APP(cons, 1), ENCARG(cons)) ENCARG(cons_app(1, 1)) -> c10(APP(1, 1), ENCARG(1)) ENCARG(cons_app(., 1)) -> c10(APP(., 1), ENCARG(.)) ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1), ENCARG(i)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (75) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (77) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, i)) -> c10(APP(encArg(x0), i), ENCARG(x0)) by ENCARG(cons_app(., i)) -> c10(APP(., i), ENCARG(.)) ENCARG(cons_app(1, i)) -> c10(APP(1, i), ENCARG(1)) ENCARG(cons_app(i, i)) -> c10(APP(i, i), ENCARG(i)) ENCARG(cons_app(map, i)) -> c10(APP(map, i), ENCARG(map)) ENCARG(cons_app(nil, i)) -> c10(APP(nil, i), ENCARG(nil)) ENCARG(cons_app(cons, i)) -> c10(APP(cons, i), ENCARG(cons)) ENCARG(cons_app(filter, i)) -> c10(APP(filter, i), ENCARG(filter)) ENCARG(cons_app(filter2, i)) -> c10(APP(filter2, i), ENCARG(filter2)) ENCARG(cons_app(true, i)) -> c10(APP(true, i), ENCARG(true)) ENCARG(cons_app(false, i)) -> c10(APP(false, i), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), i)) -> c10(APP(app(encArg(z0), encArg(z1)), i), ENCARG(cons_app(z0, z1))) ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(., i)) -> c10(APP(., i), ENCARG(.)) ENCARG(cons_app(1, i)) -> c10(APP(1, i), ENCARG(1)) ENCARG(cons_app(i, i)) -> c10(APP(i, i), ENCARG(i)) ENCARG(cons_app(map, i)) -> c10(APP(map, i), ENCARG(map)) ENCARG(cons_app(nil, i)) -> c10(APP(nil, i), ENCARG(nil)) ENCARG(cons_app(cons, i)) -> c10(APP(cons, i), ENCARG(cons)) ENCARG(cons_app(filter, i)) -> c10(APP(filter, i), ENCARG(filter)) ENCARG(cons_app(filter2, i)) -> c10(APP(filter2, i), ENCARG(filter2)) ENCARG(cons_app(true, i)) -> c10(APP(true, i), ENCARG(true)) ENCARG(cons_app(false, i)) -> c10(APP(false, i), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (79) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(true, i)) -> c10(APP(true, i), ENCARG(true)) ENCARG(cons_app(nil, i)) -> c10(APP(nil, i), ENCARG(nil)) ENCARG(cons_app(., i)) -> c10(APP(., i), ENCARG(.)) ENCARG(cons_app(filter, i)) -> c10(APP(filter, i), ENCARG(filter)) ENCARG(cons_app(1, i)) -> c10(APP(1, i), ENCARG(1)) ENCARG(cons_app(cons, i)) -> c10(APP(cons, i), ENCARG(cons)) ENCARG(cons_app(false, i)) -> c10(APP(false, i), ENCARG(false)) ENCARG(cons_app(i, i)) -> c10(APP(i, i), ENCARG(i)) ENCARG(cons_app(filter2, i)) -> c10(APP(filter2, i), ENCARG(filter2)) ENCARG(cons_app(map, i)) -> c10(APP(map, i), ENCARG(map)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (81) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, map)) -> c10(APP(encArg(x0), map), ENCARG(x0)) by ENCARG(cons_app(., map)) -> c10(APP(., map), ENCARG(.)) ENCARG(cons_app(1, map)) -> c10(APP(1, map), ENCARG(1)) ENCARG(cons_app(i, map)) -> c10(APP(i, map), ENCARG(i)) ENCARG(cons_app(map, map)) -> c10(APP(map, map), ENCARG(map)) ENCARG(cons_app(nil, map)) -> c10(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(cons, map)) -> c10(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(filter, map)) -> c10(APP(filter, map), ENCARG(filter)) ENCARG(cons_app(filter2, map)) -> c10(APP(filter2, map), ENCARG(filter2)) ENCARG(cons_app(true, map)) -> c10(APP(true, map), ENCARG(true)) ENCARG(cons_app(false, map)) -> c10(APP(false, map), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), map)) -> c10(APP(app(encArg(z0), encArg(z1)), map), ENCARG(cons_app(z0, z1))) ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(., map)) -> c10(APP(., map), ENCARG(.)) ENCARG(cons_app(1, map)) -> c10(APP(1, map), ENCARG(1)) ENCARG(cons_app(i, map)) -> c10(APP(i, map), ENCARG(i)) ENCARG(cons_app(map, map)) -> c10(APP(map, map), ENCARG(map)) ENCARG(cons_app(nil, map)) -> c10(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(cons, map)) -> c10(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(filter, map)) -> c10(APP(filter, map), ENCARG(filter)) ENCARG(cons_app(filter2, map)) -> c10(APP(filter2, map), ENCARG(filter2)) ENCARG(cons_app(true, map)) -> c10(APP(true, map), ENCARG(true)) ENCARG(cons_app(false, map)) -> c10(APP(false, map), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (83) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(., map)) -> c10(APP(., map), ENCARG(.)) ENCARG(cons_app(1, map)) -> c10(APP(1, map), ENCARG(1)) ENCARG(cons_app(true, map)) -> c10(APP(true, map), ENCARG(true)) ENCARG(cons_app(filter2, map)) -> c10(APP(filter2, map), ENCARG(filter2)) ENCARG(cons_app(nil, map)) -> c10(APP(nil, map), ENCARG(nil)) ENCARG(cons_app(map, map)) -> c10(APP(map, map), ENCARG(map)) ENCARG(cons_app(cons, map)) -> c10(APP(cons, map), ENCARG(cons)) ENCARG(cons_app(i, map)) -> c10(APP(i, map), ENCARG(i)) ENCARG(cons_app(false, map)) -> c10(APP(false, map), ENCARG(false)) ENCARG(cons_app(filter, map)) -> c10(APP(filter, map), ENCARG(filter)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (85) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, nil)) -> c10(APP(encArg(x0), nil), ENCARG(x0)) by ENCARG(cons_app(., nil)) -> c10(APP(., nil), ENCARG(.)) ENCARG(cons_app(1, nil)) -> c10(APP(1, nil), ENCARG(1)) ENCARG(cons_app(i, nil)) -> c10(APP(i, nil), ENCARG(i)) ENCARG(cons_app(map, nil)) -> c10(APP(map, nil), ENCARG(map)) ENCARG(cons_app(nil, nil)) -> c10(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c10(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(filter, nil)) -> c10(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(filter2, nil)) -> c10(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(true, nil)) -> c10(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c10(APP(false, nil), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), nil)) -> c10(APP(app(encArg(z0), encArg(z1)), nil), ENCARG(cons_app(z0, z1))) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(., nil)) -> c10(APP(., nil), ENCARG(.)) ENCARG(cons_app(1, nil)) -> c10(APP(1, nil), ENCARG(1)) ENCARG(cons_app(i, nil)) -> c10(APP(i, nil), ENCARG(i)) ENCARG(cons_app(map, nil)) -> c10(APP(map, nil), ENCARG(map)) ENCARG(cons_app(nil, nil)) -> c10(APP(nil, nil), ENCARG(nil)) ENCARG(cons_app(cons, nil)) -> c10(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(filter, nil)) -> c10(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(filter2, nil)) -> c10(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(true, nil)) -> c10(APP(true, nil), ENCARG(true)) ENCARG(cons_app(false, nil)) -> c10(APP(false, nil), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (87) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(false, nil)) -> c10(APP(false, nil), ENCARG(false)) ENCARG(cons_app(1, nil)) -> c10(APP(1, nil), ENCARG(1)) ENCARG(cons_app(filter, nil)) -> c10(APP(filter, nil), ENCARG(filter)) ENCARG(cons_app(., nil)) -> c10(APP(., nil), ENCARG(.)) ENCARG(cons_app(filter2, nil)) -> c10(APP(filter2, nil), ENCARG(filter2)) ENCARG(cons_app(map, nil)) -> c10(APP(map, nil), ENCARG(map)) ENCARG(cons_app(cons, nil)) -> c10(APP(cons, nil), ENCARG(cons)) ENCARG(cons_app(true, nil)) -> c10(APP(true, nil), ENCARG(true)) ENCARG(cons_app(i, nil)) -> c10(APP(i, nil), ENCARG(i)) ENCARG(cons_app(nil, nil)) -> c10(APP(nil, nil), ENCARG(nil)) ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, cons)) -> c10(APP(encArg(x0), cons), ENCARG(x0)) by ENCARG(cons_app(., cons)) -> c10(APP(., cons), ENCARG(.)) ENCARG(cons_app(1, cons)) -> c10(APP(1, cons), ENCARG(1)) ENCARG(cons_app(i, cons)) -> c10(APP(i, cons), ENCARG(i)) ENCARG(cons_app(map, cons)) -> c10(APP(map, cons), ENCARG(map)) ENCARG(cons_app(nil, cons)) -> c10(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c10(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(filter, cons)) -> c10(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(filter2, cons)) -> c10(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(true, cons)) -> c10(APP(true, cons), ENCARG(true)) ENCARG(cons_app(false, cons)) -> c10(APP(false, cons), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), cons)) -> c10(APP(app(encArg(z0), encArg(z1)), cons), ENCARG(cons_app(z0, z1))) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(., cons)) -> c10(APP(., cons), ENCARG(.)) ENCARG(cons_app(1, cons)) -> c10(APP(1, cons), ENCARG(1)) ENCARG(cons_app(i, cons)) -> c10(APP(i, cons), ENCARG(i)) ENCARG(cons_app(map, cons)) -> c10(APP(map, cons), ENCARG(map)) ENCARG(cons_app(nil, cons)) -> c10(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c10(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(filter, cons)) -> c10(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(filter2, cons)) -> c10(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(true, cons)) -> c10(APP(true, cons), ENCARG(true)) ENCARG(cons_app(false, cons)) -> c10(APP(false, cons), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (91) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(., cons)) -> c10(APP(., cons), ENCARG(.)) ENCARG(cons_app(filter, cons)) -> c10(APP(filter, cons), ENCARG(filter)) ENCARG(cons_app(nil, cons)) -> c10(APP(nil, cons), ENCARG(nil)) ENCARG(cons_app(cons, cons)) -> c10(APP(cons, cons), ENCARG(cons)) ENCARG(cons_app(true, cons)) -> c10(APP(true, cons), ENCARG(true)) ENCARG(cons_app(i, cons)) -> c10(APP(i, cons), ENCARG(i)) ENCARG(cons_app(false, cons)) -> c10(APP(false, cons), ENCARG(false)) ENCARG(cons_app(filter2, cons)) -> c10(APP(filter2, cons), ENCARG(filter2)) ENCARG(cons_app(map, cons)) -> c10(APP(map, cons), ENCARG(map)) ENCARG(cons_app(1, cons)) -> c10(APP(1, cons), ENCARG(1)) ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, filter)) -> c10(APP(encArg(x0), filter), ENCARG(x0)) by ENCARG(cons_app(., filter)) -> c10(APP(., filter), ENCARG(.)) ENCARG(cons_app(1, filter)) -> c10(APP(1, filter), ENCARG(1)) ENCARG(cons_app(i, filter)) -> c10(APP(i, filter), ENCARG(i)) ENCARG(cons_app(map, filter)) -> c10(APP(map, filter), ENCARG(map)) ENCARG(cons_app(nil, filter)) -> c10(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(cons, filter)) -> c10(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(filter, filter)) -> c10(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(filter2, filter)) -> c10(APP(filter2, filter), ENCARG(filter2)) ENCARG(cons_app(true, filter)) -> c10(APP(true, filter), ENCARG(true)) ENCARG(cons_app(false, filter)) -> c10(APP(false, filter), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), filter)) -> c10(APP(app(encArg(z0), encArg(z1)), filter), ENCARG(cons_app(z0, z1))) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(., filter)) -> c10(APP(., filter), ENCARG(.)) ENCARG(cons_app(1, filter)) -> c10(APP(1, filter), ENCARG(1)) ENCARG(cons_app(i, filter)) -> c10(APP(i, filter), ENCARG(i)) ENCARG(cons_app(map, filter)) -> c10(APP(map, filter), ENCARG(map)) ENCARG(cons_app(nil, filter)) -> c10(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(cons, filter)) -> c10(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(filter, filter)) -> c10(APP(filter, filter), ENCARG(filter)) ENCARG(cons_app(filter2, filter)) -> c10(APP(filter2, filter), ENCARG(filter2)) ENCARG(cons_app(true, filter)) -> c10(APP(true, filter), ENCARG(true)) ENCARG(cons_app(false, filter)) -> c10(APP(false, filter), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (95) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(1, filter)) -> c10(APP(1, filter), ENCARG(1)) ENCARG(cons_app(i, filter)) -> c10(APP(i, filter), ENCARG(i)) ENCARG(cons_app(true, filter)) -> c10(APP(true, filter), ENCARG(true)) ENCARG(cons_app(filter2, filter)) -> c10(APP(filter2, filter), ENCARG(filter2)) ENCARG(cons_app(map, filter)) -> c10(APP(map, filter), ENCARG(map)) ENCARG(cons_app(false, filter)) -> c10(APP(false, filter), ENCARG(false)) ENCARG(cons_app(., filter)) -> c10(APP(., filter), ENCARG(.)) ENCARG(cons_app(cons, filter)) -> c10(APP(cons, filter), ENCARG(cons)) ENCARG(cons_app(nil, filter)) -> c10(APP(nil, filter), ENCARG(nil)) ENCARG(cons_app(filter, filter)) -> c10(APP(filter, filter), ENCARG(filter)) ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, filter2)) -> c10(APP(encArg(x0), filter2), ENCARG(x0)) by ENCARG(cons_app(., filter2)) -> c10(APP(., filter2), ENCARG(.)) ENCARG(cons_app(1, filter2)) -> c10(APP(1, filter2), ENCARG(1)) ENCARG(cons_app(i, filter2)) -> c10(APP(i, filter2), ENCARG(i)) ENCARG(cons_app(map, filter2)) -> c10(APP(map, filter2), ENCARG(map)) ENCARG(cons_app(nil, filter2)) -> c10(APP(nil, filter2), ENCARG(nil)) ENCARG(cons_app(cons, filter2)) -> c10(APP(cons, filter2), ENCARG(cons)) ENCARG(cons_app(filter, filter2)) -> c10(APP(filter, filter2), ENCARG(filter)) ENCARG(cons_app(filter2, filter2)) -> c10(APP(filter2, filter2), ENCARG(filter2)) ENCARG(cons_app(true, filter2)) -> c10(APP(true, filter2), ENCARG(true)) ENCARG(cons_app(false, filter2)) -> c10(APP(false, filter2), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), filter2)) -> c10(APP(app(encArg(z0), encArg(z1)), filter2), ENCARG(cons_app(z0, z1))) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(., filter2)) -> c10(APP(., filter2), ENCARG(.)) ENCARG(cons_app(1, filter2)) -> c10(APP(1, filter2), ENCARG(1)) ENCARG(cons_app(i, filter2)) -> c10(APP(i, filter2), ENCARG(i)) ENCARG(cons_app(map, filter2)) -> c10(APP(map, filter2), ENCARG(map)) ENCARG(cons_app(nil, filter2)) -> c10(APP(nil, filter2), ENCARG(nil)) ENCARG(cons_app(cons, filter2)) -> c10(APP(cons, filter2), ENCARG(cons)) ENCARG(cons_app(filter, filter2)) -> c10(APP(filter, filter2), ENCARG(filter)) ENCARG(cons_app(filter2, filter2)) -> c10(APP(filter2, filter2), ENCARG(filter2)) ENCARG(cons_app(true, filter2)) -> c10(APP(true, filter2), ENCARG(true)) ENCARG(cons_app(false, filter2)) -> c10(APP(false, filter2), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(1, filter2)) -> c10(APP(1, filter2), ENCARG(1)) ENCARG(cons_app(i, filter2)) -> c10(APP(i, filter2), ENCARG(i)) ENCARG(cons_app(false, filter2)) -> c10(APP(false, filter2), ENCARG(false)) ENCARG(cons_app(filter, filter2)) -> c10(APP(filter, filter2), ENCARG(filter)) ENCARG(cons_app(filter2, filter2)) -> c10(APP(filter2, filter2), ENCARG(filter2)) ENCARG(cons_app(map, filter2)) -> c10(APP(map, filter2), ENCARG(map)) ENCARG(cons_app(., filter2)) -> c10(APP(., filter2), ENCARG(.)) ENCARG(cons_app(true, filter2)) -> c10(APP(true, filter2), ENCARG(true)) ENCARG(cons_app(cons, filter2)) -> c10(APP(cons, filter2), ENCARG(cons)) ENCARG(cons_app(nil, filter2)) -> c10(APP(nil, filter2), ENCARG(nil)) ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, true)) -> c10(APP(encArg(x0), true), ENCARG(x0)) by ENCARG(cons_app(., true)) -> c10(APP(., true), ENCARG(.)) ENCARG(cons_app(1, true)) -> c10(APP(1, true), ENCARG(1)) ENCARG(cons_app(i, true)) -> c10(APP(i, true), ENCARG(i)) ENCARG(cons_app(map, true)) -> c10(APP(map, true), ENCARG(map)) ENCARG(cons_app(nil, true)) -> c10(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c10(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(filter, true)) -> c10(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(filter2, true)) -> c10(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(true, true)) -> c10(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c10(APP(false, true), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), true)) -> c10(APP(app(encArg(z0), encArg(z1)), true), ENCARG(cons_app(z0, z1))) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(., true)) -> c10(APP(., true), ENCARG(.)) ENCARG(cons_app(1, true)) -> c10(APP(1, true), ENCARG(1)) ENCARG(cons_app(i, true)) -> c10(APP(i, true), ENCARG(i)) ENCARG(cons_app(map, true)) -> c10(APP(map, true), ENCARG(map)) ENCARG(cons_app(nil, true)) -> c10(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(cons, true)) -> c10(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(filter, true)) -> c10(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(filter2, true)) -> c10(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(true, true)) -> c10(APP(true, true), ENCARG(true)) ENCARG(cons_app(false, true)) -> c10(APP(false, true), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (103) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(filter, true)) -> c10(APP(filter, true), ENCARG(filter)) ENCARG(cons_app(cons, true)) -> c10(APP(cons, true), ENCARG(cons)) ENCARG(cons_app(1, true)) -> c10(APP(1, true), ENCARG(1)) ENCARG(cons_app(filter2, true)) -> c10(APP(filter2, true), ENCARG(filter2)) ENCARG(cons_app(map, true)) -> c10(APP(map, true), ENCARG(map)) ENCARG(cons_app(., true)) -> c10(APP(., true), ENCARG(.)) ENCARG(cons_app(true, true)) -> c10(APP(true, true), ENCARG(true)) ENCARG(cons_app(nil, true)) -> c10(APP(nil, true), ENCARG(nil)) ENCARG(cons_app(i, true)) -> c10(APP(i, true), ENCARG(i)) ENCARG(cons_app(false, true)) -> c10(APP(false, true), ENCARG(false)) ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_2, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(x0, false)) -> c10(APP(encArg(x0), false), ENCARG(x0)) by ENCARG(cons_app(., false)) -> c10(APP(., false), ENCARG(.)) ENCARG(cons_app(1, false)) -> c10(APP(1, false), ENCARG(1)) ENCARG(cons_app(i, false)) -> c10(APP(i, false), ENCARG(i)) ENCARG(cons_app(map, false)) -> c10(APP(map, false), ENCARG(map)) ENCARG(cons_app(nil, false)) -> c10(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c10(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter, false)) -> c10(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(filter2, false)) -> c10(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(true, false)) -> c10(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c10(APP(false, false), ENCARG(false)) ENCARG(cons_app(cons_app(z0, z1), false)) -> c10(APP(app(encArg(z0), encArg(z1)), false), ENCARG(cons_app(z0, z1))) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(., false)) -> c10(APP(., false), ENCARG(.)) ENCARG(cons_app(1, false)) -> c10(APP(1, false), ENCARG(1)) ENCARG(cons_app(i, false)) -> c10(APP(i, false), ENCARG(i)) ENCARG(cons_app(map, false)) -> c10(APP(map, false), ENCARG(map)) ENCARG(cons_app(nil, false)) -> c10(APP(nil, false), ENCARG(nil)) ENCARG(cons_app(cons, false)) -> c10(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(filter, false)) -> c10(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(filter2, false)) -> c10(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(true, false)) -> c10(APP(true, false), ENCARG(true)) ENCARG(cons_app(false, false)) -> c10(APP(false, false), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c10_2, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCARG(cons_app(filter2, false)) -> c10(APP(filter2, false), ENCARG(filter2)) ENCARG(cons_app(map, false)) -> c10(APP(map, false), ENCARG(map)) ENCARG(cons_app(false, false)) -> c10(APP(false, false), ENCARG(false)) ENCARG(cons_app(i, false)) -> c10(APP(i, false), ENCARG(i)) ENCARG(cons_app(1, false)) -> c10(APP(1, false), ENCARG(1)) ENCARG(cons_app(., false)) -> c10(APP(., false), ENCARG(.)) ENCARG(cons_app(filter, false)) -> c10(APP(filter, false), ENCARG(filter)) ENCARG(cons_app(true, false)) -> c10(APP(true, false), ENCARG(true)) ENCARG(cons_app(cons, false)) -> c10(APP(cons, false), ENCARG(cons)) ENCARG(cons_app(nil, false)) -> c10(APP(nil, false), ENCARG(nil)) ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c10_2, c31_3, c31_2, c35_2, c35_1, c_1, c10_3 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCARG(cons_app(i, x1)) -> c10(APP(i, encArg(x1)), ENCARG(x1)) by ENCARG(cons_app(i, .)) -> c10(APP(i, .), ENCARG(.)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1), ENCARG(1)) ENCARG(cons_app(i, i)) -> c10(APP(i, i), ENCARG(i)) ENCARG(cons_app(i, map)) -> c10(APP(i, map), ENCARG(map)) ENCARG(cons_app(i, nil)) -> c10(APP(i, nil), ENCARG(nil)) ENCARG(cons_app(i, cons)) -> c10(APP(i, cons), ENCARG(cons)) ENCARG(cons_app(i, filter)) -> c10(APP(i, filter), ENCARG(filter)) ENCARG(cons_app(i, filter2)) -> c10(APP(i, filter2), ENCARG(filter2)) ENCARG(cons_app(i, true)) -> c10(APP(i, true), ENCARG(true)) ENCARG(cons_app(i, false)) -> c10(APP(i, false), ENCARG(false)) ENCARG(cons_app(i, cons_app(z0, z1))) -> c10(APP(i, app(encArg(z0), encArg(z1))), ENCARG(cons_app(z0, z1))) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(i, .)) -> c10(APP(i, .), ENCARG(.)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1), ENCARG(1)) ENCARG(cons_app(i, i)) -> c10(APP(i, i), ENCARG(i)) ENCARG(cons_app(i, map)) -> c10(APP(i, map), ENCARG(map)) ENCARG(cons_app(i, nil)) -> c10(APP(i, nil), ENCARG(nil)) ENCARG(cons_app(i, cons)) -> c10(APP(i, cons), ENCARG(cons)) ENCARG(cons_app(i, filter)) -> c10(APP(i, filter), ENCARG(filter)) ENCARG(cons_app(i, filter2)) -> c10(APP(i, filter2), ENCARG(filter2)) ENCARG(cons_app(i, true)) -> c10(APP(i, true), ENCARG(true)) ENCARG(cons_app(i, false)) -> c10(APP(i, false), ENCARG(false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 9 trailing nodes: ENCARG(cons_app(i, true)) -> c10(APP(i, true), ENCARG(true)) ENCARG(cons_app(i, cons)) -> c10(APP(i, cons), ENCARG(cons)) ENCARG(cons_app(i, filter2)) -> c10(APP(i, filter2), ENCARG(filter2)) ENCARG(cons_app(i, nil)) -> c10(APP(i, nil), ENCARG(nil)) ENCARG(cons_app(i, map)) -> c10(APP(i, map), ENCARG(map)) ENCARG(cons_app(i, .)) -> c10(APP(i, .), ENCARG(.)) ENCARG(cons_app(i, false)) -> c10(APP(i, false), ENCARG(false)) ENCARG(cons_app(i, filter)) -> c10(APP(i, filter), ENCARG(filter)) ENCARG(cons_app(i, i)) -> c10(APP(i, i), ENCARG(i)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1), ENCARG(1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (115) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2), APP(app(., app(app(., z0), z1)), z2)) by APP(app(filter, app(., app(app(., app(i, app(app(., x1), x2))), x1))), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, 1), app(., app(app(., app(i, app(app(., x1), x2))), x1))), x2), x3), APP(app(., app(app(., app(i, app(app(., x1), x2))), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z0)), app(., app(app(., x0), z0))), 1), x3), APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., app(i, app(app(., x1), x2))), x1))), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, 1), app(., app(app(., app(i, app(app(., x1), x2))), x1))), x2), x3), APP(app(., app(app(., app(i, app(app(., x1), x2))), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z0)), app(., app(app(., x0), z0))), 1), x3), APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., app(i, app(app(., x1), x2))), x1))), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, 1), app(., app(app(., app(i, app(app(., x1), x2))), x1))), x2), x3), APP(app(., app(app(., app(i, app(app(., x1), x2))), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z0)), app(., app(app(., x0), z0))), 1), x3), APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (117) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: APP(app(filter, app(., app(app(., app(i, app(app(., x1), x2))), x1))), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, 1), app(., app(app(., app(i, app(app(., x1), x2))), x1))), x2), x3), APP(app(., app(app(., app(i, app(app(., x1), x2))), x1)), x2)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z0)), app(., app(app(., x0), z0))), 1), x3), APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z0)), app(., app(app(., x0), z0))), 1), x3), APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (119) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (121) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2), APP(i, app(app(., z0), z1))) by APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (123) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2), APP(app(filter, z0), app(app(cons, z1), z2))) by APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), app(., app(i, z0))), z0), x2)), app(filter, app(., app(i, z0)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), app(., z0)), app(i, z0)), x2)), app(filter, app(., z0))), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), i), 1), x2)), app(filter, i)), app(app(cons, 1), x2)), x3), APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(map, z0)), nil), x2)), app(filter, app(map, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(map, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(filter, z0)), nil), x2)), app(filter, app(filter, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), app(., app(i, z0))), z0), x2)), app(filter, app(., app(i, z0)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), app(., z0)), app(i, z0)), x2)), app(filter, app(., z0))), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), i), 1), x2)), app(filter, i)), app(app(cons, 1), x2)), x3), APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(map, z0)), nil), x2)), app(filter, app(map, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(map, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(filter, z0)), nil), x2)), app(filter, app(filter, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, z1), app(app(filter, z0), z2))), app(app(app(filter2, true), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), app(., app(i, z0))), z0), x2)), app(filter, app(., app(i, z0)))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), app(., z0)), app(i, z0)), x2)), app(filter, app(., z0))), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, 1), i), 1), x2)), app(filter, i)), app(app(cons, 1), x2)), x3), APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(map, z0)), nil), x2)), app(filter, app(map, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(cons, app(z0, z1)), app(app(map, z0), z2))), app(map, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(map, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, nil), app(filter, z0)), nil), x2)), app(filter, app(filter, z0))), app(app(cons, nil), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (125) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 7 trailing tuple parts ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (127) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2), APP(app(app(app(filter2, false), z0), z1), z2)) by APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, nil), app(app(app(filter2, false), z0), x1)), nil), x3), APP(app(app(app(filter2, false), z0), x1), nil)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, nil), app(app(app(filter2, false), z0), x1)), nil), x3), APP(app(app(app(filter2, false), z0), x1), nil)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, nil), app(app(app(filter2, false), z0), x1)), nil), x3), APP(app(app(app(filter2, false), z0), x1), nil)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, .) -> c(APP(encArg(x0), .)) by ENCODE_APP(., .) -> c(APP(., .)) ENCODE_APP(1, .) -> c(APP(1, .)) ENCODE_APP(i, .) -> c(APP(i, .)) ENCODE_APP(map, .) -> c(APP(map, .)) ENCODE_APP(nil, .) -> c(APP(nil, .)) ENCODE_APP(cons, .) -> c(APP(cons, .)) ENCODE_APP(filter, .) -> c(APP(filter, .)) ENCODE_APP(filter2, .) -> c(APP(filter2, .)) ENCODE_APP(true, .) -> c(APP(true, .)) ENCODE_APP(false, .) -> c(APP(false, .)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(., .) -> c(APP(., .)) ENCODE_APP(1, .) -> c(APP(1, .)) ENCODE_APP(i, .) -> c(APP(i, .)) ENCODE_APP(map, .) -> c(APP(map, .)) ENCODE_APP(nil, .) -> c(APP(nil, .)) ENCODE_APP(cons, .) -> c(APP(cons, .)) ENCODE_APP(filter, .) -> c(APP(filter, .)) ENCODE_APP(filter2, .) -> c(APP(filter2, .)) ENCODE_APP(true, .) -> c(APP(true, .)) ENCODE_APP(false, .) -> c(APP(false, .)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(., .) -> c(APP(., .)) ENCODE_APP(true, .) -> c(APP(true, .)) ENCODE_APP(filter2, .) -> c(APP(filter2, .)) ENCODE_APP(map, .) -> c(APP(map, .)) ENCODE_APP(filter, .) -> c(APP(filter, .)) ENCODE_APP(cons, .) -> c(APP(cons, .)) ENCODE_APP(1, .) -> c(APP(1, .)) ENCODE_APP(i, .) -> c(APP(i, .)) ENCODE_APP(nil, .) -> c(APP(nil, .)) ENCODE_APP(false, .) -> c(APP(false, .)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (135) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, 1) -> c(APP(encArg(x0), 1)) by ENCODE_APP(., 1) -> c(APP(., 1)) ENCODE_APP(1, 1) -> c(APP(1, 1)) ENCODE_APP(i, 1) -> c(APP(i, 1)) ENCODE_APP(map, 1) -> c(APP(map, 1)) ENCODE_APP(nil, 1) -> c(APP(nil, 1)) ENCODE_APP(cons, 1) -> c(APP(cons, 1)) ENCODE_APP(filter, 1) -> c(APP(filter, 1)) ENCODE_APP(filter2, 1) -> c(APP(filter2, 1)) ENCODE_APP(true, 1) -> c(APP(true, 1)) ENCODE_APP(false, 1) -> c(APP(false, 1)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(., 1) -> c(APP(., 1)) ENCODE_APP(1, 1) -> c(APP(1, 1)) ENCODE_APP(i, 1) -> c(APP(i, 1)) ENCODE_APP(map, 1) -> c(APP(map, 1)) ENCODE_APP(nil, 1) -> c(APP(nil, 1)) ENCODE_APP(cons, 1) -> c(APP(cons, 1)) ENCODE_APP(filter, 1) -> c(APP(filter, 1)) ENCODE_APP(filter2, 1) -> c(APP(filter2, 1)) ENCODE_APP(true, 1) -> c(APP(true, 1)) ENCODE_APP(false, 1) -> c(APP(false, 1)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (137) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ENCODE_APP(i, 1) -> c(APP(i, 1)) Removed 9 trailing nodes: ENCODE_APP(true, 1) -> c(APP(true, 1)) ENCODE_APP(filter, 1) -> c(APP(filter, 1)) ENCODE_APP(1, 1) -> c(APP(1, 1)) ENCODE_APP(filter2, 1) -> c(APP(filter2, 1)) ENCODE_APP(map, 1) -> c(APP(map, 1)) ENCODE_APP(., 1) -> c(APP(., 1)) ENCODE_APP(false, 1) -> c(APP(false, 1)) ENCODE_APP(cons, 1) -> c(APP(cons, 1)) ENCODE_APP(nil, 1) -> c(APP(nil, 1)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (139) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, i) -> c(APP(encArg(x0), i)) by ENCODE_APP(., i) -> c(APP(., i)) ENCODE_APP(1, i) -> c(APP(1, i)) ENCODE_APP(i, i) -> c(APP(i, i)) ENCODE_APP(map, i) -> c(APP(map, i)) ENCODE_APP(nil, i) -> c(APP(nil, i)) ENCODE_APP(cons, i) -> c(APP(cons, i)) ENCODE_APP(filter, i) -> c(APP(filter, i)) ENCODE_APP(filter2, i) -> c(APP(filter2, i)) ENCODE_APP(true, i) -> c(APP(true, i)) ENCODE_APP(false, i) -> c(APP(false, i)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(., i) -> c(APP(., i)) ENCODE_APP(1, i) -> c(APP(1, i)) ENCODE_APP(i, i) -> c(APP(i, i)) ENCODE_APP(map, i) -> c(APP(map, i)) ENCODE_APP(nil, i) -> c(APP(nil, i)) ENCODE_APP(cons, i) -> c(APP(cons, i)) ENCODE_APP(filter, i) -> c(APP(filter, i)) ENCODE_APP(filter2, i) -> c(APP(filter2, i)) ENCODE_APP(true, i) -> c(APP(true, i)) ENCODE_APP(false, i) -> c(APP(false, i)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (141) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(filter2, i) -> c(APP(filter2, i)) ENCODE_APP(map, i) -> c(APP(map, i)) ENCODE_APP(., i) -> c(APP(., i)) ENCODE_APP(false, i) -> c(APP(false, i)) ENCODE_APP(filter, i) -> c(APP(filter, i)) ENCODE_APP(true, i) -> c(APP(true, i)) ENCODE_APP(1, i) -> c(APP(1, i)) ENCODE_APP(i, i) -> c(APP(i, i)) ENCODE_APP(cons, i) -> c(APP(cons, i)) ENCODE_APP(nil, i) -> c(APP(nil, i)) ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, map) -> c(APP(encArg(x0), map)) by ENCODE_APP(., map) -> c(APP(., map)) ENCODE_APP(1, map) -> c(APP(1, map)) ENCODE_APP(i, map) -> c(APP(i, map)) ENCODE_APP(map, map) -> c(APP(map, map)) ENCODE_APP(nil, map) -> c(APP(nil, map)) ENCODE_APP(cons, map) -> c(APP(cons, map)) ENCODE_APP(filter, map) -> c(APP(filter, map)) ENCODE_APP(filter2, map) -> c(APP(filter2, map)) ENCODE_APP(true, map) -> c(APP(true, map)) ENCODE_APP(false, map) -> c(APP(false, map)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(., map) -> c(APP(., map)) ENCODE_APP(1, map) -> c(APP(1, map)) ENCODE_APP(i, map) -> c(APP(i, map)) ENCODE_APP(map, map) -> c(APP(map, map)) ENCODE_APP(nil, map) -> c(APP(nil, map)) ENCODE_APP(cons, map) -> c(APP(cons, map)) ENCODE_APP(filter, map) -> c(APP(filter, map)) ENCODE_APP(filter2, map) -> c(APP(filter2, map)) ENCODE_APP(true, map) -> c(APP(true, map)) ENCODE_APP(false, map) -> c(APP(false, map)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (145) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(., map) -> c(APP(., map)) ENCODE_APP(true, map) -> c(APP(true, map)) ENCODE_APP(filter2, map) -> c(APP(filter2, map)) ENCODE_APP(map, map) -> c(APP(map, map)) ENCODE_APP(i, map) -> c(APP(i, map)) ENCODE_APP(nil, map) -> c(APP(nil, map)) ENCODE_APP(filter, map) -> c(APP(filter, map)) ENCODE_APP(cons, map) -> c(APP(cons, map)) ENCODE_APP(1, map) -> c(APP(1, map)) ENCODE_APP(false, map) -> c(APP(false, map)) ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, nil) -> c(APP(encArg(x0), nil)) by ENCODE_APP(., nil) -> c(APP(., nil)) ENCODE_APP(1, nil) -> c(APP(1, nil)) ENCODE_APP(i, nil) -> c(APP(i, nil)) ENCODE_APP(map, nil) -> c(APP(map, nil)) ENCODE_APP(nil, nil) -> c(APP(nil, nil)) ENCODE_APP(cons, nil) -> c(APP(cons, nil)) ENCODE_APP(filter, nil) -> c(APP(filter, nil)) ENCODE_APP(filter2, nil) -> c(APP(filter2, nil)) ENCODE_APP(true, nil) -> c(APP(true, nil)) ENCODE_APP(false, nil) -> c(APP(false, nil)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(., nil) -> c(APP(., nil)) ENCODE_APP(1, nil) -> c(APP(1, nil)) ENCODE_APP(i, nil) -> c(APP(i, nil)) ENCODE_APP(map, nil) -> c(APP(map, nil)) ENCODE_APP(nil, nil) -> c(APP(nil, nil)) ENCODE_APP(cons, nil) -> c(APP(cons, nil)) ENCODE_APP(filter, nil) -> c(APP(filter, nil)) ENCODE_APP(filter2, nil) -> c(APP(filter2, nil)) ENCODE_APP(true, nil) -> c(APP(true, nil)) ENCODE_APP(false, nil) -> c(APP(false, nil)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(false, nil) -> c(APP(false, nil)) ENCODE_APP(1, nil) -> c(APP(1, nil)) ENCODE_APP(., nil) -> c(APP(., nil)) ENCODE_APP(cons, nil) -> c(APP(cons, nil)) ENCODE_APP(filter2, nil) -> c(APP(filter2, nil)) ENCODE_APP(map, nil) -> c(APP(map, nil)) ENCODE_APP(filter, nil) -> c(APP(filter, nil)) ENCODE_APP(i, nil) -> c(APP(i, nil)) ENCODE_APP(true, nil) -> c(APP(true, nil)) ENCODE_APP(nil, nil) -> c(APP(nil, nil)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (151) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, cons) -> c(APP(encArg(x0), cons)) by ENCODE_APP(., cons) -> c(APP(., cons)) ENCODE_APP(1, cons) -> c(APP(1, cons)) ENCODE_APP(i, cons) -> c(APP(i, cons)) ENCODE_APP(map, cons) -> c(APP(map, cons)) ENCODE_APP(nil, cons) -> c(APP(nil, cons)) ENCODE_APP(cons, cons) -> c(APP(cons, cons)) ENCODE_APP(filter, cons) -> c(APP(filter, cons)) ENCODE_APP(filter2, cons) -> c(APP(filter2, cons)) ENCODE_APP(true, cons) -> c(APP(true, cons)) ENCODE_APP(false, cons) -> c(APP(false, cons)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(., cons) -> c(APP(., cons)) ENCODE_APP(1, cons) -> c(APP(1, cons)) ENCODE_APP(i, cons) -> c(APP(i, cons)) ENCODE_APP(map, cons) -> c(APP(map, cons)) ENCODE_APP(nil, cons) -> c(APP(nil, cons)) ENCODE_APP(cons, cons) -> c(APP(cons, cons)) ENCODE_APP(filter, cons) -> c(APP(filter, cons)) ENCODE_APP(filter2, cons) -> c(APP(filter2, cons)) ENCODE_APP(true, cons) -> c(APP(true, cons)) ENCODE_APP(false, cons) -> c(APP(false, cons)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (153) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(filter2, cons) -> c(APP(filter2, cons)) ENCODE_APP(map, cons) -> c(APP(map, cons)) ENCODE_APP(i, cons) -> c(APP(i, cons)) ENCODE_APP(false, cons) -> c(APP(false, cons)) ENCODE_APP(1, cons) -> c(APP(1, cons)) ENCODE_APP(cons, cons) -> c(APP(cons, cons)) ENCODE_APP(., cons) -> c(APP(., cons)) ENCODE_APP(true, cons) -> c(APP(true, cons)) ENCODE_APP(nil, cons) -> c(APP(nil, cons)) ENCODE_APP(filter, cons) -> c(APP(filter, cons)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (155) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, filter) -> c(APP(encArg(x0), filter)) by ENCODE_APP(., filter) -> c(APP(., filter)) ENCODE_APP(1, filter) -> c(APP(1, filter)) ENCODE_APP(i, filter) -> c(APP(i, filter)) ENCODE_APP(map, filter) -> c(APP(map, filter)) ENCODE_APP(nil, filter) -> c(APP(nil, filter)) ENCODE_APP(cons, filter) -> c(APP(cons, filter)) ENCODE_APP(filter, filter) -> c(APP(filter, filter)) ENCODE_APP(filter2, filter) -> c(APP(filter2, filter)) ENCODE_APP(true, filter) -> c(APP(true, filter)) ENCODE_APP(false, filter) -> c(APP(false, filter)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(., filter) -> c(APP(., filter)) ENCODE_APP(1, filter) -> c(APP(1, filter)) ENCODE_APP(i, filter) -> c(APP(i, filter)) ENCODE_APP(map, filter) -> c(APP(map, filter)) ENCODE_APP(nil, filter) -> c(APP(nil, filter)) ENCODE_APP(cons, filter) -> c(APP(cons, filter)) ENCODE_APP(filter, filter) -> c(APP(filter, filter)) ENCODE_APP(filter2, filter) -> c(APP(filter2, filter)) ENCODE_APP(true, filter) -> c(APP(true, filter)) ENCODE_APP(false, filter) -> c(APP(false, filter)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (157) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(i, filter) -> c(APP(i, filter)) ENCODE_APP(filter2, filter) -> c(APP(filter2, filter)) ENCODE_APP(map, filter) -> c(APP(map, filter)) ENCODE_APP(false, filter) -> c(APP(false, filter)) ENCODE_APP(1, filter) -> c(APP(1, filter)) ENCODE_APP(., filter) -> c(APP(., filter)) ENCODE_APP(true, filter) -> c(APP(true, filter)) ENCODE_APP(filter, filter) -> c(APP(filter, filter)) ENCODE_APP(nil, filter) -> c(APP(nil, filter)) ENCODE_APP(cons, filter) -> c(APP(cons, filter)) ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, filter2) -> c(APP(encArg(x0), filter2)) by ENCODE_APP(., filter2) -> c(APP(., filter2)) ENCODE_APP(1, filter2) -> c(APP(1, filter2)) ENCODE_APP(i, filter2) -> c(APP(i, filter2)) ENCODE_APP(map, filter2) -> c(APP(map, filter2)) ENCODE_APP(nil, filter2) -> c(APP(nil, filter2)) ENCODE_APP(cons, filter2) -> c(APP(cons, filter2)) ENCODE_APP(filter, filter2) -> c(APP(filter, filter2)) ENCODE_APP(filter2, filter2) -> c(APP(filter2, filter2)) ENCODE_APP(true, filter2) -> c(APP(true, filter2)) ENCODE_APP(false, filter2) -> c(APP(false, filter2)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(., filter2) -> c(APP(., filter2)) ENCODE_APP(1, filter2) -> c(APP(1, filter2)) ENCODE_APP(i, filter2) -> c(APP(i, filter2)) ENCODE_APP(map, filter2) -> c(APP(map, filter2)) ENCODE_APP(nil, filter2) -> c(APP(nil, filter2)) ENCODE_APP(cons, filter2) -> c(APP(cons, filter2)) ENCODE_APP(filter, filter2) -> c(APP(filter, filter2)) ENCODE_APP(filter2, filter2) -> c(APP(filter2, filter2)) ENCODE_APP(true, filter2) -> c(APP(true, filter2)) ENCODE_APP(false, filter2) -> c(APP(false, filter2)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(1, filter2) -> c(APP(1, filter2)) ENCODE_APP(false, filter2) -> c(APP(false, filter2)) ENCODE_APP(filter, filter2) -> c(APP(filter, filter2)) ENCODE_APP(cons, filter2) -> c(APP(cons, filter2)) ENCODE_APP(true, filter2) -> c(APP(true, filter2)) ENCODE_APP(filter2, filter2) -> c(APP(filter2, filter2)) ENCODE_APP(map, filter2) -> c(APP(map, filter2)) ENCODE_APP(nil, filter2) -> c(APP(nil, filter2)) ENCODE_APP(i, filter2) -> c(APP(i, filter2)) ENCODE_APP(., filter2) -> c(APP(., filter2)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (163) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, true) -> c(APP(encArg(x0), true)) by ENCODE_APP(., true) -> c(APP(., true)) ENCODE_APP(1, true) -> c(APP(1, true)) ENCODE_APP(i, true) -> c(APP(i, true)) ENCODE_APP(map, true) -> c(APP(map, true)) ENCODE_APP(nil, true) -> c(APP(nil, true)) ENCODE_APP(cons, true) -> c(APP(cons, true)) ENCODE_APP(filter, true) -> c(APP(filter, true)) ENCODE_APP(filter2, true) -> c(APP(filter2, true)) ENCODE_APP(true, true) -> c(APP(true, true)) ENCODE_APP(false, true) -> c(APP(false, true)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) ENCODE_APP(., true) -> c(APP(., true)) ENCODE_APP(1, true) -> c(APP(1, true)) ENCODE_APP(i, true) -> c(APP(i, true)) ENCODE_APP(map, true) -> c(APP(map, true)) ENCODE_APP(nil, true) -> c(APP(nil, true)) ENCODE_APP(cons, true) -> c(APP(cons, true)) ENCODE_APP(filter, true) -> c(APP(filter, true)) ENCODE_APP(filter2, true) -> c(APP(filter2, true)) ENCODE_APP(true, true) -> c(APP(true, true)) ENCODE_APP(false, true) -> c(APP(false, true)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (165) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(true, true) -> c(APP(true, true)) ENCODE_APP(filter2, true) -> c(APP(filter2, true)) ENCODE_APP(map, true) -> c(APP(map, true)) ENCODE_APP(nil, true) -> c(APP(nil, true)) ENCODE_APP(false, true) -> c(APP(false, true)) ENCODE_APP(1, true) -> c(APP(1, true)) ENCODE_APP(., true) -> c(APP(., true)) ENCODE_APP(filter, true) -> c(APP(filter, true)) ENCODE_APP(cons, true) -> c(APP(cons, true)) ENCODE_APP(i, true) -> c(APP(i, true)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (167) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, false) -> c(APP(encArg(x0), false)) by ENCODE_APP(., false) -> c(APP(., false)) ENCODE_APP(1, false) -> c(APP(1, false)) ENCODE_APP(i, false) -> c(APP(i, false)) ENCODE_APP(map, false) -> c(APP(map, false)) ENCODE_APP(nil, false) -> c(APP(nil, false)) ENCODE_APP(cons, false) -> c(APP(cons, false)) ENCODE_APP(filter, false) -> c(APP(filter, false)) ENCODE_APP(filter2, false) -> c(APP(filter2, false)) ENCODE_APP(true, false) -> c(APP(true, false)) ENCODE_APP(false, false) -> c(APP(false, false)) ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false)) ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) ENCODE_APP(cons_app(z0, z1), true) -> c(APP(app(encArg(z0), encArg(z1)), true)) ENCODE_APP(., false) -> c(APP(., false)) ENCODE_APP(1, false) -> c(APP(1, false)) ENCODE_APP(i, false) -> c(APP(i, false)) ENCODE_APP(map, false) -> c(APP(map, false)) ENCODE_APP(nil, false) -> c(APP(nil, false)) ENCODE_APP(cons, false) -> c(APP(cons, false)) ENCODE_APP(filter, false) -> c(APP(filter, false)) ENCODE_APP(filter2, false) -> c(APP(filter2, false)) ENCODE_APP(true, false) -> c(APP(true, false)) ENCODE_APP(false, false) -> c(APP(false, false)) ENCODE_APP(cons_app(z0, z1), false) -> c(APP(app(encArg(z0), encArg(z1)), false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (169) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 10 trailing nodes: ENCODE_APP(filter, false) -> c(APP(filter, false)) ENCODE_APP(nil, false) -> c(APP(nil, false)) ENCODE_APP(., false) -> c(APP(., false)) ENCODE_APP(true, false) -> c(APP(true, false)) ENCODE_APP(false, false) -> c(APP(false, false)) ENCODE_APP(cons, false) -> c(APP(cons, false)) ENCODE_APP(i, false) -> c(APP(i, false)) ENCODE_APP(1, false) -> c(APP(1, false)) ENCODE_APP(filter2, false) -> c(APP(filter2, false)) ENCODE_APP(map, false) -> c(APP(map, false)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (171) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(x0, cons_app(z0, z1)) -> c(APP(encArg(x0), app(encArg(z0), encArg(z1)))) by ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(., cons_app(x1, x2)) -> c(APP(., app(encArg(x1), encArg(x2)))) ENCODE_APP(1, cons_app(x1, x2)) -> c(APP(1, app(encArg(x1), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2)))) ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2)))) ENCODE_APP(filter, cons_app(x1, x2)) -> c(APP(filter, app(encArg(x1), encArg(x2)))) ENCODE_APP(filter2, cons_app(x1, x2)) -> c(APP(filter2, app(encArg(x1), encArg(x2)))) ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2)))) ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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)) ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(., cons_app(x1, x2)) -> c(APP(., app(encArg(x1), encArg(x2)))) ENCODE_APP(1, cons_app(x1, x2)) -> c(APP(1, app(encArg(x1), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2)))) ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2)))) ENCODE_APP(filter, cons_app(x1, x2)) -> c(APP(filter, app(encArg(x1), encArg(x2)))) ENCODE_APP(filter2, cons_app(x1, x2)) -> c(APP(filter2, app(encArg(x1), encArg(x2)))) ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2)))) ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (173) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 9 trailing nodes: ENCODE_APP(map, cons_app(x1, x2)) -> c(APP(map, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons, cons_app(x1, x2)) -> c(APP(cons, app(encArg(x1), encArg(x2)))) ENCODE_APP(false, cons_app(x1, x2)) -> c(APP(false, app(encArg(x1), encArg(x2)))) ENCODE_APP(filter2, cons_app(x1, x2)) -> c(APP(filter2, app(encArg(x1), encArg(x2)))) ENCODE_APP(filter, cons_app(x1, x2)) -> c(APP(filter, app(encArg(x1), encArg(x2)))) ENCODE_APP(1, cons_app(x1, x2)) -> c(APP(1, app(encArg(x1), encArg(x2)))) ENCODE_APP(true, cons_app(x1, x2)) -> c(APP(true, app(encArg(x1), encArg(x2)))) ENCODE_APP(., cons_app(x1, x2)) -> c(APP(., app(encArg(x1), encArg(x2)))) ENCODE_APP(nil, cons_app(x1, x2)) -> c(APP(nil, app(encArg(x1), encArg(x2)))) ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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)) ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(i, x1) -> c(APP(i, encArg(x1))) by ENCODE_APP(i, .) -> c(APP(i, .)) ENCODE_APP(i, 1) -> c(APP(i, 1)) ENCODE_APP(i, i) -> c(APP(i, i)) ENCODE_APP(i, map) -> c(APP(i, map)) ENCODE_APP(i, nil) -> c(APP(i, nil)) ENCODE_APP(i, cons) -> c(APP(i, cons)) ENCODE_APP(i, filter) -> c(APP(i, filter)) ENCODE_APP(i, filter2) -> c(APP(i, filter2)) ENCODE_APP(i, true) -> c(APP(i, true)) ENCODE_APP(i, false) -> c(APP(i, false)) ENCODE_APP(i, cons_app(z0, z1)) -> c(APP(i, app(encArg(z0), encArg(z1)))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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)) ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) ENCODE_APP(i, .) -> c(APP(i, .)) ENCODE_APP(i, 1) -> c(APP(i, 1)) ENCODE_APP(i, i) -> c(APP(i, i)) ENCODE_APP(i, map) -> c(APP(i, map)) ENCODE_APP(i, nil) -> c(APP(i, nil)) ENCODE_APP(i, cons) -> c(APP(i, cons)) ENCODE_APP(i, filter) -> c(APP(i, filter)) ENCODE_APP(i, filter2) -> c(APP(i, filter2)) ENCODE_APP(i, true) -> c(APP(i, true)) ENCODE_APP(i, false) -> c(APP(i, false)) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (177) CdtLeafRemovalProof (ComplexityIfPolyImplication) Removed 1 leading nodes: ENCODE_APP(i, 1) -> c(APP(i, 1)) Removed 9 trailing nodes: ENCODE_APP(i, cons) -> c(APP(i, cons)) ENCODE_APP(i, filter) -> c(APP(i, filter)) ENCODE_APP(i, nil) -> c(APP(i, nil)) ENCODE_APP(i, filter2) -> c(APP(i, filter2)) ENCODE_APP(i, map) -> c(APP(i, map)) ENCODE_APP(i, .) -> c(APP(i, .)) ENCODE_APP(i, true) -> c(APP(i, true)) ENCODE_APP(i, false) -> c(APP(i, false)) ENCODE_APP(i, i) -> c(APP(i, i)) ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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)) ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c_1, c10_3, c10_2 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace ENCODE_APP(cons_app(z0, z1), x1) -> c(APP(app(encArg(z0), encArg(z1)), encArg(x1))) by ENCODE_APP(cons_app(x0, x1), .) -> c(APP(app(encArg(x0), encArg(x1)), .)) ENCODE_APP(cons_app(x0, x1), 1) -> c(APP(app(encArg(x0), encArg(x1)), 1)) ENCODE_APP(cons_app(x0, x1), i) -> c(APP(app(encArg(x0), encArg(x1)), i)) ENCODE_APP(cons_app(x0, x1), map) -> c(APP(app(encArg(x0), encArg(x1)), map)) ENCODE_APP(cons_app(x0, x1), nil) -> c(APP(app(encArg(x0), encArg(x1)), nil)) ENCODE_APP(cons_app(x0, x1), cons) -> c(APP(app(encArg(x0), encArg(x1)), cons)) ENCODE_APP(cons_app(x0, x1), filter) -> c(APP(app(encArg(x0), encArg(x1)), filter)) ENCODE_APP(cons_app(x0, x1), filter2) -> c(APP(app(encArg(x0), encArg(x1)), filter2)) ENCODE_APP(cons_app(x0, x1), true) -> c(APP(app(encArg(x0), encArg(x1)), true)) ENCODE_APP(cons_app(x0, x1), false) -> c(APP(app(encArg(x0), encArg(x1)), false)) ENCODE_APP(cons_app(x0, x1), cons_app(z0, z1)) -> c(APP(app(encArg(x0), encArg(x1)), app(encArg(z0), encArg(z1)))) ENCODE_APP(cons_app(x0, .), x2) -> c(APP(app(encArg(x0), .), encArg(x2))) ENCODE_APP(cons_app(x0, 1), x2) -> c(APP(app(encArg(x0), 1), encArg(x2))) ENCODE_APP(cons_app(x0, i), x2) -> c(APP(app(encArg(x0), i), encArg(x2))) ENCODE_APP(cons_app(x0, map), x2) -> c(APP(app(encArg(x0), map), encArg(x2))) ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2))) ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2))) ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2))) ENCODE_APP(cons_app(x0, filter2), x2) -> c(APP(app(encArg(x0), filter2), encArg(x2))) ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2))) ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2))) ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_APP(cons_app(., x1), x2) -> c(APP(app(., encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(1, x1), x2) -> c(APP(app(1, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(i, x1), x2) -> c(APP(app(i, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(map, x1), x2) -> c(APP(app(map, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(filter2, x1), x2) -> c(APP(app(filter2, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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)) ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(x0, .), x2) -> c(APP(app(encArg(x0), .), encArg(x2))) ENCODE_APP(cons_app(x0, 1), x2) -> c(APP(app(encArg(x0), 1), encArg(x2))) ENCODE_APP(cons_app(x0, i), x2) -> c(APP(app(encArg(x0), i), encArg(x2))) ENCODE_APP(cons_app(x0, map), x2) -> c(APP(app(encArg(x0), map), encArg(x2))) ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2))) ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2))) ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2))) ENCODE_APP(cons_app(x0, filter2), x2) -> c(APP(app(encArg(x0), filter2), encArg(x2))) ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2))) ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2))) ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_APP(cons_app(., x1), x2) -> c(APP(app(., encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(1, x1), x2) -> c(APP(app(1, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(i, x1), x2) -> c(APP(app(i, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(map, x1), x2) -> c(APP(app(map, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(filter2, x1), x2) -> c(APP(app(filter2, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c10_3, c10_2, c_1 ---------------------------------------- (181) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 6 trailing nodes: ENCODE_APP(cons_app(filter2, x1), x2) -> c(APP(app(filter2, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(true, x1), x2) -> c(APP(app(true, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(cons, x1), x2) -> c(APP(app(cons, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(nil, x1), x2) -> c(APP(app(nil, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(1, x1), x2) -> c(APP(app(1, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(false, x1), x2) -> c(APP(app(false, encArg(x1)), encArg(x2))) ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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)) ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(x0, .), x2) -> c(APP(app(encArg(x0), .), encArg(x2))) ENCODE_APP(cons_app(x0, 1), x2) -> c(APP(app(encArg(x0), 1), encArg(x2))) ENCODE_APP(cons_app(x0, i), x2) -> c(APP(app(encArg(x0), i), encArg(x2))) ENCODE_APP(cons_app(x0, map), x2) -> c(APP(app(encArg(x0), map), encArg(x2))) ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2))) ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2))) ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2))) ENCODE_APP(cons_app(x0, filter2), x2) -> c(APP(app(encArg(x0), filter2), encArg(x2))) ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2))) ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2))) ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_APP(cons_app(., x1), x2) -> c(APP(app(., encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(i, x1), x2) -> c(APP(app(i, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(map, x1), x2) -> c(APP(app(map, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c10_3, c10_2, c_1 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace APP(app(filter, i), app(app(cons, app(app(., x0), app(i, z0))), x2)) -> c35(APP(app(app(app(filter2, app(app(., z0), app(i, x0))), i), app(app(., x0), app(i, z0))), x2), APP(i, app(app(., x0), app(i, z0)))) by APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), app(i, x1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., x1), z0)), i), app(app(., app(i, z0)), app(i, x1))), x2), APP(i, app(app(., app(i, z0)), app(i, x1)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, x1))), x2)) -> c35(APP(i, app(app(., x0), app(i, x1)))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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)) ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(x0, .), x2) -> c(APP(app(encArg(x0), .), encArg(x2))) ENCODE_APP(cons_app(x0, 1), x2) -> c(APP(app(encArg(x0), 1), encArg(x2))) ENCODE_APP(cons_app(x0, i), x2) -> c(APP(app(encArg(x0), i), encArg(x2))) ENCODE_APP(cons_app(x0, map), x2) -> c(APP(app(encArg(x0), map), encArg(x2))) ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2))) ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2))) ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2))) ENCODE_APP(cons_app(x0, filter2), x2) -> c(APP(app(encArg(x0), filter2), encArg(x2))) ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2))) ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2))) ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_APP(cons_app(., x1), x2) -> c(APP(app(., encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(i, x1), x2) -> c(APP(app(i, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(map, x1), x2) -> c(APP(app(map, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), app(i, x1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., x1), z0)), i), app(app(., app(i, z0)), app(i, x1))), x2), APP(i, app(app(., app(i, z0)), app(i, x1)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, x1))), x2)) -> c35(APP(i, app(app(., x0), app(i, x1)))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), app(i, x1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., x1), z0)), i), app(app(., app(i, z0)), app(i, x1))), x2), APP(i, app(app(., app(i, z0)), app(i, x1)))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, x1))), x2)) -> c35(APP(i, app(app(., x0), app(i, x1)))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c10_3, c10_2, c_1 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: encArg(.) -> . encArg(1) -> 1 encArg(i) -> i encArg(map) -> map encArg(nil) -> nil encArg(cons) -> cons encArg(filter) -> filter encArg(filter2) -> filter2 encArg(true) -> true encArg(false) -> false encArg(cons_app(z0, z1)) -> app(encArg(z0), encArg(z1)) app(app(., 1), z0) -> z0 app(app(., z0), 1) -> z0 app(app(., app(i, z0)), z0) -> 1 app(app(., z0), app(i, z0)) -> 1 app(app(., app(i, z0)), app(app(., z0), z1)) -> z1 app(app(., z0), app(app(., app(i, z0)), z1)) -> z1 app(app(., app(app(., z0), z1)), z2) -> app(app(., z0), app(app(., z1), z2)) app(i, 1) -> 1 app(i, app(i, z0)) -> z0 app(i, app(app(., z0), z1)) -> app(app(., app(i, z1)), app(i, z0)) app(app(map, z0), nil) -> nil app(app(map, z0), app(app(cons, z1), z2)) -> app(app(cons, app(z0, z1)), app(app(map, z0), z2)) app(app(filter, z0), nil) -> nil app(app(filter, z0), app(app(cons, z1), z2)) -> app(app(app(app(filter2, app(z0, z1)), z0), z1), z2) app(app(app(app(filter2, true), z0), z1), z2) -> app(app(cons, z1), app(app(filter, z0), z2)) app(app(app(app(filter2, false), z0), z1), z2) -> app(app(filter, z0), z2) Tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) ENCARG(cons_app(., x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(1, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(map, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(nil, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(cons, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(filter2, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(true, x1)) -> c10(ENCARG(x1)) ENCARG(cons_app(false, x1)) -> c10(ENCARG(x1)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) ENCARG(cons_app(x0, cons_app(x1, .))) -> c10(APP(encArg(x0), app(encArg(x1), .)), ENCARG(x0), ENCARG(cons_app(x1, .))) ENCARG(cons_app(x0, cons_app(x1, 1))) -> c10(APP(encArg(x0), app(encArg(x1), 1)), ENCARG(x0), ENCARG(cons_app(x1, 1))) ENCARG(cons_app(x0, cons_app(x1, i))) -> c10(APP(encArg(x0), app(encArg(x1), i)), ENCARG(x0), ENCARG(cons_app(x1, i))) ENCARG(cons_app(x0, cons_app(x1, map))) -> c10(APP(encArg(x0), app(encArg(x1), map)), ENCARG(x0), ENCARG(cons_app(x1, map))) ENCARG(cons_app(x0, cons_app(x1, nil))) -> c10(APP(encArg(x0), app(encArg(x1), nil)), ENCARG(x0), ENCARG(cons_app(x1, nil))) ENCARG(cons_app(x0, cons_app(x1, cons))) -> c10(APP(encArg(x0), app(encArg(x1), cons)), ENCARG(x0), ENCARG(cons_app(x1, cons))) ENCARG(cons_app(x0, cons_app(x1, filter))) -> c10(APP(encArg(x0), app(encArg(x1), filter)), ENCARG(x0), ENCARG(cons_app(x1, filter))) ENCARG(cons_app(x0, cons_app(x1, filter2))) -> c10(APP(encArg(x0), app(encArg(x1), filter2)), ENCARG(x0), ENCARG(cons_app(x1, filter2))) ENCARG(cons_app(x0, cons_app(x1, true))) -> c10(APP(encArg(x0), app(encArg(x1), true)), ENCARG(x0), ENCARG(cons_app(x1, true))) ENCARG(cons_app(x0, cons_app(x1, false))) -> c10(APP(encArg(x0), app(encArg(x1), false)), ENCARG(x0), ENCARG(cons_app(x1, false))) ENCARG(cons_app(x0, cons_app(x1, cons_app(z0, z1)))) -> c10(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(., x2))) -> c10(APP(encArg(x0), app(., encArg(x2))), ENCARG(x0), ENCARG(cons_app(., x2))) ENCARG(cons_app(x0, cons_app(1, x2))) -> c10(APP(encArg(x0), app(1, encArg(x2))), ENCARG(x0), ENCARG(cons_app(1, x2))) ENCARG(cons_app(x0, cons_app(i, x2))) -> c10(APP(encArg(x0), app(i, encArg(x2))), ENCARG(x0), ENCARG(cons_app(i, x2))) ENCARG(cons_app(x0, cons_app(map, x2))) -> c10(APP(encArg(x0), app(map, encArg(x2))), ENCARG(x0), ENCARG(cons_app(map, x2))) ENCARG(cons_app(x0, cons_app(nil, x2))) -> c10(APP(encArg(x0), app(nil, encArg(x2))), ENCARG(x0), ENCARG(cons_app(nil, x2))) ENCARG(cons_app(x0, cons_app(cons, x2))) -> c10(APP(encArg(x0), app(cons, encArg(x2))), ENCARG(x0), ENCARG(cons_app(cons, x2))) ENCARG(cons_app(x0, cons_app(filter, x2))) -> c10(APP(encArg(x0), app(filter, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter, x2))) ENCARG(cons_app(x0, cons_app(filter2, x2))) -> c10(APP(encArg(x0), app(filter2, encArg(x2))), ENCARG(x0), ENCARG(cons_app(filter2, x2))) ENCARG(cons_app(x0, cons_app(true, x2))) -> c10(APP(encArg(x0), app(true, encArg(x2))), ENCARG(x0), ENCARG(cons_app(true, x2))) ENCARG(cons_app(x0, cons_app(false, x2))) -> c10(APP(encArg(x0), app(false, encArg(x2))), ENCARG(x0), ENCARG(cons_app(false, x2))) ENCARG(cons_app(x0, cons_app(cons_app(z0, z1), x2))) -> c10(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))) -> c10(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2))), ENCARG(cons_app(z0, z1)), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(., cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(1, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(i, cons_app(x1, x2))) -> c10(APP(i, app(encArg(x1), encArg(x2))), ENCARG(cons_app(x1, x2))) ENCARG(cons_app(map, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(nil, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(filter2, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(true, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(false, cons_app(x1, x2))) -> c10(ENCARG(cons_app(x1, x2))) ENCARG(cons_app(cons_app(x0, .), x2)) -> c10(APP(app(encArg(x0), .), encArg(x2)), ENCARG(cons_app(x0, .)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, 1), x2)) -> c10(APP(app(encArg(x0), 1), encArg(x2)), ENCARG(cons_app(x0, 1)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, i), x2)) -> c10(APP(app(encArg(x0), i), encArg(x2)), ENCARG(cons_app(x0, i)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, map), x2)) -> c10(APP(app(encArg(x0), map), encArg(x2)), ENCARG(cons_app(x0, map)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, nil), x2)) -> c10(APP(app(encArg(x0), nil), encArg(x2)), ENCARG(cons_app(x0, nil)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons), x2)) -> c10(APP(app(encArg(x0), cons), encArg(x2)), ENCARG(cons_app(x0, cons)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter), x2)) -> c10(APP(app(encArg(x0), filter), encArg(x2)), ENCARG(cons_app(x0, filter)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, filter2), x2)) -> c10(APP(app(encArg(x0), filter2), encArg(x2)), ENCARG(cons_app(x0, filter2)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, true), x2)) -> c10(APP(app(encArg(x0), true), encArg(x2)), ENCARG(cons_app(x0, true)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, false), x2)) -> c10(APP(app(encArg(x0), false), encArg(x2)), ENCARG(cons_app(x0, false)), ENCARG(x2)) ENCARG(cons_app(cons_app(x0, cons_app(z0, z1)), x2)) -> c10(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(., x1), x2)) -> c10(APP(app(., encArg(x1)), encArg(x2)), ENCARG(cons_app(., x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(i, x1), x2)) -> c10(APP(app(i, encArg(x1)), encArg(x2)), ENCARG(cons_app(i, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(map, x1), x2)) -> c10(APP(app(map, encArg(x1)), encArg(x2)), ENCARG(cons_app(map, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter, x1), x2)) -> c10(APP(app(filter, encArg(x1)), encArg(x2)), ENCARG(cons_app(filter, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons_app(z0, z1), x1), x2)) -> c10(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), .)) -> c10(APP(app(encArg(x0), encArg(x1)), .), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), 1)) -> c10(APP(app(encArg(x0), encArg(x1)), 1), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), i)) -> c10(APP(app(encArg(x0), encArg(x1)), i), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), map)) -> c10(APP(app(encArg(x0), encArg(x1)), map), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), nil)) -> c10(APP(app(encArg(x0), encArg(x1)), nil), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), cons)) -> c10(APP(app(encArg(x0), encArg(x1)), cons), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter)) -> c10(APP(app(encArg(x0), encArg(x1)), filter), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), filter2)) -> c10(APP(app(encArg(x0), encArg(x1)), filter2), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), true)) -> c10(APP(app(encArg(x0), encArg(x1)), true), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(x0, x1), false)) -> c10(APP(app(encArg(x0), encArg(x1)), false), ENCARG(cons_app(x0, x1))) ENCARG(cons_app(cons_app(1, x1), x2)) -> c10(ENCARG(cons_app(1, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(nil, x1), x2)) -> c10(ENCARG(cons_app(nil, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(cons, x1), x2)) -> c10(ENCARG(cons_app(cons, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(filter2, x1), x2)) -> c10(ENCARG(cons_app(filter2, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(true, x1), x2)) -> c10(ENCARG(cons_app(true, x1)), ENCARG(x2)) ENCARG(cons_app(cons_app(false, x1), x2)) -> c10(ENCARG(cons_app(false, x1)), ENCARG(x2)) ENCARG(cons_app(i, 1)) -> c10(APP(i, 1)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) ENCODE_APP(cons_app(z0, z1), .) -> c(APP(app(encArg(z0), encArg(z1)), .)) ENCODE_APP(cons_app(z0, z1), 1) -> c(APP(app(encArg(z0), encArg(z1)), 1)) ENCODE_APP(cons_app(z0, z1), i) -> c(APP(app(encArg(z0), encArg(z1)), i)) ENCODE_APP(cons_app(z0, z1), map) -> c(APP(app(encArg(z0), encArg(z1)), map)) ENCODE_APP(cons_app(z0, z1), nil) -> c(APP(app(encArg(z0), encArg(z1)), nil)) ENCODE_APP(cons_app(z0, z1), cons) -> c(APP(app(encArg(z0), encArg(z1)), cons)) ENCODE_APP(cons_app(z0, z1), filter) -> c(APP(app(encArg(z0), encArg(z1)), filter)) ENCODE_APP(cons_app(z0, z1), filter2) -> c(APP(app(encArg(z0), encArg(z1)), filter2)) 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)) ENCODE_APP(x0, cons_app(x1, .)) -> c(APP(encArg(x0), app(encArg(x1), .))) ENCODE_APP(x0, cons_app(x1, 1)) -> c(APP(encArg(x0), app(encArg(x1), 1))) ENCODE_APP(x0, cons_app(x1, i)) -> c(APP(encArg(x0), app(encArg(x1), i))) ENCODE_APP(x0, cons_app(x1, map)) -> c(APP(encArg(x0), app(encArg(x1), map))) ENCODE_APP(x0, cons_app(x1, nil)) -> c(APP(encArg(x0), app(encArg(x1), nil))) ENCODE_APP(x0, cons_app(x1, cons)) -> c(APP(encArg(x0), app(encArg(x1), cons))) ENCODE_APP(x0, cons_app(x1, filter)) -> c(APP(encArg(x0), app(encArg(x1), filter))) ENCODE_APP(x0, cons_app(x1, filter2)) -> c(APP(encArg(x0), app(encArg(x1), filter2))) ENCODE_APP(x0, cons_app(x1, true)) -> c(APP(encArg(x0), app(encArg(x1), true))) ENCODE_APP(x0, cons_app(x1, false)) -> c(APP(encArg(x0), app(encArg(x1), false))) ENCODE_APP(x0, cons_app(x1, cons_app(z0, z1))) -> c(APP(encArg(x0), app(encArg(x1), app(encArg(z0), encArg(z1))))) ENCODE_APP(x0, cons_app(., x2)) -> c(APP(encArg(x0), app(., encArg(x2)))) ENCODE_APP(x0, cons_app(1, x2)) -> c(APP(encArg(x0), app(1, encArg(x2)))) ENCODE_APP(x0, cons_app(i, x2)) -> c(APP(encArg(x0), app(i, encArg(x2)))) ENCODE_APP(x0, cons_app(map, x2)) -> c(APP(encArg(x0), app(map, encArg(x2)))) ENCODE_APP(x0, cons_app(nil, x2)) -> c(APP(encArg(x0), app(nil, encArg(x2)))) ENCODE_APP(x0, cons_app(cons, x2)) -> c(APP(encArg(x0), app(cons, encArg(x2)))) ENCODE_APP(x0, cons_app(filter, x2)) -> c(APP(encArg(x0), app(filter, encArg(x2)))) ENCODE_APP(x0, cons_app(filter2, x2)) -> c(APP(encArg(x0), app(filter2, encArg(x2)))) ENCODE_APP(x0, cons_app(true, x2)) -> c(APP(encArg(x0), app(true, encArg(x2)))) ENCODE_APP(x0, cons_app(false, x2)) -> c(APP(encArg(x0), app(false, encArg(x2)))) ENCODE_APP(x0, cons_app(cons_app(z0, z1), x2)) -> c(APP(encArg(x0), app(app(encArg(z0), encArg(z1)), encArg(x2)))) ENCODE_APP(i, cons_app(x1, x2)) -> c(APP(i, app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(z0, z1), cons_app(x1, x2)) -> c(APP(app(encArg(z0), encArg(z1)), app(encArg(x1), encArg(x2)))) ENCODE_APP(cons_app(x0, .), x2) -> c(APP(app(encArg(x0), .), encArg(x2))) ENCODE_APP(cons_app(x0, 1), x2) -> c(APP(app(encArg(x0), 1), encArg(x2))) ENCODE_APP(cons_app(x0, i), x2) -> c(APP(app(encArg(x0), i), encArg(x2))) ENCODE_APP(cons_app(x0, map), x2) -> c(APP(app(encArg(x0), map), encArg(x2))) ENCODE_APP(cons_app(x0, nil), x2) -> c(APP(app(encArg(x0), nil), encArg(x2))) ENCODE_APP(cons_app(x0, cons), x2) -> c(APP(app(encArg(x0), cons), encArg(x2))) ENCODE_APP(cons_app(x0, filter), x2) -> c(APP(app(encArg(x0), filter), encArg(x2))) ENCODE_APP(cons_app(x0, filter2), x2) -> c(APP(app(encArg(x0), filter2), encArg(x2))) ENCODE_APP(cons_app(x0, true), x2) -> c(APP(app(encArg(x0), true), encArg(x2))) ENCODE_APP(cons_app(x0, false), x2) -> c(APP(app(encArg(x0), false), encArg(x2))) ENCODE_APP(cons_app(x0, cons_app(z0, z1)), x2) -> c(APP(app(encArg(x0), app(encArg(z0), encArg(z1))), encArg(x2))) ENCODE_APP(cons_app(., x1), x2) -> c(APP(app(., encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(i, x1), x2) -> c(APP(app(i, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(map, x1), x2) -> c(APP(app(map, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(filter, x1), x2) -> c(APP(app(filter, encArg(x1)), encArg(x2))) ENCODE_APP(cons_app(cons_app(z0, z1), x1), x2) -> c(APP(app(app(encArg(z0), encArg(z1)), encArg(x1)), encArg(x2))) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, x1))), x2)) -> c35(APP(i, app(app(., x0), app(i, x1)))) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), app(i, x1))), x2)) -> c35(APP(i, app(app(., app(i, z0)), app(i, x1)))) S tuples: APP(app(., 1), z0) -> c22 APP(app(., z0), 1) -> c23 APP(app(., app(i, z0)), z0) -> c24 APP(app(., z0), app(i, z0)) -> c25 APP(app(., app(i, z0)), app(app(., z0), z1)) -> c26 APP(app(., z0), app(app(., app(i, z0)), z1)) -> c27 APP(i, 1) -> c29 APP(i, app(i, z0)) -> c30 APP(app(map, z0), nil) -> c32 APP(app(filter, z0), nil) -> c34 APP(app(., app(app(., z0), z1)), z2) -> c28(APP(app(., z0), app(app(., z1), z2)), APP(app(., z1), z2)) APP(app(map, z0), app(app(cons, z1), z2)) -> c33(APP(z0, z1), APP(app(map, z0), z2)) APP(app(app(app(filter2, true), z0), z1), z2) -> c36(APP(app(filter, z0), z2)) APP(app(app(app(filter2, false), z0), z1), z2) -> c37(APP(app(filter, z0), z2)) APP(i, app(app(., app(i, z0)), x1)) -> c31(APP(app(., app(i, x1)), z0), APP(i, x1), APP(i, app(i, z0))) APP(i, app(app(., x0), app(i, z0))) -> c31(APP(app(., z0), app(i, x0)), APP(i, app(i, z0)), APP(i, x0)) APP(i, app(app(., x0), app(app(., z0), z1))) -> c31(APP(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0)), APP(i, app(app(., z0), z1)), APP(i, x0)) APP(i, app(app(., x0), x1)) -> c31(APP(i, x1), APP(i, x0)) APP(app(filter, app(., 1)), app(app(cons, z0), x2)) -> c35(APP(app(app(app(filter2, z0), app(., 1)), z0), x2), APP(app(., 1), z0)) APP(app(filter, app(., z0)), app(app(cons, 1), x2)) -> c35(APP(app(app(app(filter2, z0), app(., z0)), 1), x2), APP(app(., z0), 1)) APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2), APP(app(., app(i, z0)), app(app(., z0), z1))) APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2)) -> c35(APP(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2), APP(app(., z0), app(app(., app(i, z0)), z1))) APP(app(filter, i), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(app(app(filter2, z0), i), app(i, z0)), x2), APP(i, app(i, z0))) APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2)) -> c35(APP(app(., app(i, z0)), z0)) APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2)) -> c35(APP(app(., z0), app(i, z0))) APP(app(filter, i), app(app(cons, 1), x2)) -> c35(APP(i, 1)) APP(app(filter, app(map, z0)), app(app(cons, nil), x2)) -> c35(APP(app(map, z0), nil)) APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2)) -> c35(APP(app(map, z0), app(app(cons, z1), z2))) APP(app(filter, app(filter, z0)), app(app(cons, nil), x2)) -> c35(APP(app(filter, z0), nil)) APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2)) -> c35(APP(app(app(app(filter2, true), z0), z1), z2)) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, z0), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), app(i, z0)))), z0), x3), APP(app(., app(app(., x0), app(i, z0))), z0)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(i, z0)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), 1)), app(., app(app(., x0), z0))), app(i, z0)), x3), APP(app(., app(app(., x0), z0)), app(i, z0))) APP(app(filter, app(., app(app(., x0), app(i, z0)))), app(app(cons, app(app(., z0), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), app(i, z0)))), app(app(., z0), z1)), x3), APP(app(., app(app(., x0), app(i, z0))), app(app(., z0), z1))) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, app(app(., app(i, z0)), z1)), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), z1)), app(., app(app(., x0), z0))), app(app(., app(i, z0)), z1)), x3), APP(app(., app(app(., x0), z0)), app(app(., app(i, z0)), z1))) APP(app(filter, app(., app(app(., x0), app(app(., z0), z1)))), app(app(cons, z2), x3)) -> c35(APP(app(app(app(filter2, app(app(., x0), app(app(., z0), app(app(., z1), z2)))), app(., app(app(., x0), app(app(., z0), z1)))), z2), x3), APP(app(., app(app(., x0), app(app(., z0), z1))), z2)) APP(app(filter, app(., app(app(., x0), x1))), app(app(cons, x2), x3)) -> c35(APP(app(., app(app(., x0), x1)), x2)) APP(app(filter, app(., app(app(., x0), z0))), app(app(cons, 1), x3)) -> c35(APP(app(., app(app(., x0), z0)), 1)) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), x1)), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(i, x1)), z0)), i), app(app(., app(i, z0)), x1)), x2), APP(i, app(app(., app(i, z0)), x1))) APP(app(filter, i), app(app(cons, app(app(., x0), app(app(., z0), z1))), x2)) -> c35(APP(app(app(app(filter2, app(app(., app(app(., app(i, z1)), app(i, z0))), app(i, x0))), i), app(app(., x0), app(app(., z0), z1))), x2), APP(i, app(app(., x0), app(app(., z0), z1)))) APP(app(filter, i), app(app(cons, app(app(., x0), x1)), x2)) -> c35(APP(i, app(app(., x0), x1))) APP(app(filter, app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(filter, z0), z2)), app(app(app(filter2, false), z0), z1)), z2), x2)), app(filter, app(app(app(filter2, false), z0), z1))), app(app(cons, z2), x2)), x3), APP(app(filter, app(app(app(filter2, false), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., 1))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., 1)), z0), x2)), app(filter, app(., 1))), app(app(cons, z0), x2)), x3), APP(app(filter, app(., 1)), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), app(., z0)), 1), x2)), app(filter, app(., z0))), app(app(cons, 1), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., app(i, z0))), app(app(., z0), z1)), x2)), app(filter, app(., app(i, z0)))), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, app(., app(i, z0))), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z1), app(., z0)), app(app(., app(i, z0)), z1)), x2)), app(filter, app(., z0))), app(app(cons, app(app(., app(i, z0)), z1)), x2)), x3), APP(app(filter, app(., z0)), app(app(cons, app(app(., app(i, z0)), z1)), x2))) APP(app(filter, app(filter, app(., app(app(., z0), z1)))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., z0), app(app(., z1), z2))), app(., app(app(., z0), z1))), z2), x2)), app(filter, app(., app(app(., z0), z1)))), app(app(cons, z2), x2)), x3), APP(app(filter, app(., app(app(., z0), z1))), app(app(cons, z2), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, z0), i), app(i, z0)), x2)), app(filter, i)), app(app(cons, app(i, z0)), x2)), x3), APP(app(filter, i), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, app(app(., z0), z1)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(., app(i, z1)), app(i, z0))), i), app(app(., z0), z1)), x2)), app(filter, i)), app(app(cons, app(app(., z0), z1)), x2)), x3), APP(app(filter, i), app(app(cons, app(app(., z0), z1)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(filter, z0)), app(app(cons, z1), z2)), x2)), app(filter, app(filter, z0))), app(app(cons, app(app(cons, z1), z2)), x2)), x3), APP(app(filter, app(filter, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(app(app(filter2, true), z0), z1))), app(app(cons, app(app(cons, z2), x2)), x3)) -> c35(APP(app(filter, app(app(app(filter2, true), z0), z1)), app(app(cons, z2), x2))) APP(app(filter, app(filter, app(., app(i, z0)))), app(app(cons, app(app(cons, z0), x2)), x3)) -> c35(APP(app(filter, app(., app(i, z0))), app(app(cons, z0), x2))) APP(app(filter, app(filter, app(., z0))), app(app(cons, app(app(cons, app(i, z0)), x2)), x3)) -> c35(APP(app(filter, app(., z0)), app(app(cons, app(i, z0)), x2))) APP(app(filter, app(filter, i)), app(app(cons, app(app(cons, 1), x2)), x3)) -> c35(APP(app(filter, i), app(app(cons, 1), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, nil), x2))) APP(app(filter, app(filter, app(map, z0))), app(app(cons, app(app(cons, app(app(cons, z1), z2)), x2)), x3)) -> c35(APP(app(filter, app(map, z0)), app(app(cons, app(app(cons, z1), z2)), x2))) APP(app(filter, app(filter, app(filter, z0))), app(app(cons, app(app(cons, nil), x2)), x3)) -> c35(APP(app(filter, app(filter, z0)), app(app(cons, nil), x2))) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, app(app(cons, z1), z2)), x3)) -> c35(APP(app(app(app(filter2, app(app(app(app(filter2, app(z0, z1)), z0), z1), z2)), app(app(app(filter2, false), z0), x1)), app(app(cons, z1), z2)), x3), APP(app(app(app(filter2, false), z0), x1), app(app(cons, z1), z2))) APP(app(filter, app(app(app(filter2, false), x0), x1)), app(app(cons, x2), x3)) -> c35(APP(app(app(app(filter2, false), x0), x1), x2)) APP(app(filter, app(app(app(filter2, false), z0), x1)), app(app(cons, nil), x3)) -> c35(APP(app(app(app(filter2, false), z0), x1), nil)) APP(app(filter, i), app(app(cons, app(app(., x0), app(i, x1))), x2)) -> c35(APP(i, app(app(., x0), app(i, x1)))) APP(app(filter, i), app(app(cons, app(app(., app(i, z0)), app(i, x1))), x2)) -> c35(APP(i, app(app(., app(i, z0)), app(i, x1)))) K tuples:none Defined Rule Symbols: encArg_1, app_2 Defined Pair Symbols: APP_2, ENCARG_1, ENCODE_APP_2 Compound Symbols: c22, c23, c24, c25, c26, c27, c29, c30, c32, c34, c28_2, c33_2, c36_1, c37_1, c10_1, c31_3, c31_2, c35_2, c35_1, c10_3, c10_2, c_1